diff --git a/PyGitUp/git_wrapper.py b/PyGitUp/git_wrapper.py
index 40d4181..de7b6da 100644
--- a/PyGitUp/git_wrapper.py
+++ b/PyGitUp/git_wrapper.py
@@ -8,7 +8,7 @@
 """
 
 
-__all__ = ['GitWrapper', 'GitError']
+__all__ = ['GitWrapper', 'GitError', 'UnresolvedConflictError']
 
 ###############################################################################
 # IMPORTS
@@ -144,9 +144,11 @@ def stash():
 
             stashed[0] = True
 
+        stash.suppress_pop = False
+
         yield stash
 
-        if stashed[0]:
+        if stashed[0] and not stash.suppress_pop:
             print(colored('unstashing', 'magenta'))
             try:
                 self._run('stash', 'pop')
@@ -341,3 +343,19 @@ def __init__(self, current_branch, target_branch, **kwargs):
             current_branch, target_branch
         )
         GitError.__init__(self, message, **kwargs)
+
+
+class UnresolvedConflictError(GitError):
+    """
+    Rebase conflict could not be resolved. Repo left in conflicted state.
+    """
+
+    def __init__(self, branch_name, target_branch, repo_path, **kwargs):
+        kwargs.pop('message', None)
+        message = (
+            f"Failed to resolve rebase conflicts for {branch_name} "
+            f"onto {target_branch}.\n"
+            f"The repo at {repo_path} is left in a conflicted state.\n"
+            f"Resolve manually, then run: git rebase --continue"
+        )
+        GitError.__init__(self, message, **kwargs)
diff --git a/PyGitUp/gitup.py b/PyGitUp/gitup.py
index fd97e64..dbf526d 100644
--- a/PyGitUp/gitup.py
+++ b/PyGitUp/gitup.py
@@ -15,6 +15,7 @@
 import os
 import re
 import json
+import shlex
 import subprocess
 from io import StringIO
 from tempfile import NamedTemporaryFile
@@ -38,7 +39,8 @@
 
 # PyGitUp libs
 from PyGitUp.utils import execute, uniq, find
-from PyGitUp.git_wrapper import GitWrapper, GitError
+from PyGitUp.git_wrapper import GitWrapper, GitError, RebaseError, \
+    UnresolvedConflictError
 
 ON_WINDOWS = sys.platform == 'win32'
 
@@ -98,6 +100,7 @@ class GitUp:
         'rebase.arguments': None,
         'rebase.auto': True,
         'rebase.log-hook': None,
+        'rebase.conflict-resolver': None,
         'updates.check': True,
         'push.auto': False,
         'push.tags': False,
@@ -296,7 +299,16 @@ def rebase_all_branches(self):
                 else:
                     stasher()
                     self.git.checkout(branch.name)
-                    self.git.rebase(target)
+                    try:
+                        self.git.rebase(target)
+                    except RebaseError:
+                        if self._try_resolve_conflicts(
+                            branch.name, target.name,
+                            self.repo.working_dir
+                        ):
+                            continue
+                        stasher.suppress_pop = True
+                        raise
 
             if (self.repo.head.is_detached  # Only on Travis CI,
                     # we get a detached head after doing our rebase *confused*.
@@ -306,6 +318,84 @@ def rebase_all_branches(self):
                               'magenta'))
                 original_branch.checkout()
 
+    def _build_resolver_prompt(self, branch_name, target_name, repo_path):
+        """Build the default prompt with conflict context."""
+        try:
+            result = subprocess.run(
+                ['git', 'diff', '--name-only', '--diff-filter=U'],
+                cwd=repo_path, capture_output=True, text=True
+            )
+            conflicted = result.stdout.strip()
+        except Exception:
+            conflicted = '(unable to determine)'
+
+        return (
+            f"Resolve the git rebase conflicts in this repository.\n\n"
+            f"Branch '{branch_name}' is being rebased onto "
+            f"'{target_name}'.\n\n"
+            f"Conflicted files:\n{conflicted}\n\n"
+            f"Steps:\n"
+            f"1. Read each conflicted file and resolve the conflict "
+            f"markers\n"
+            f"2. Stage resolved files with `git add`\n"
+            f"3. Run `git rebase --continue`\n"
+            f"4. If further conflicts arise, repeat steps 1-3\n"
+            f"5. Exit when the rebase is fully complete"
+        )
+
+    def _try_resolve_conflicts(self, branch_name, target_name, repo_path):
+        """
+        Invoke the configured conflict resolver command.
+
+        Returns True if the resolver succeeded and rebase completed.
+        Returns False if no resolver is configured.
+        Raises UnresolvedConflictError if the resolver failed.
+        """
+        resolver_template = self.settings['rebase.conflict-resolver']
+        if not resolver_template:
+            return False
+
+        print(colored('invoking conflict resolver...', 'yellow'))
+
+        prompt = self._build_resolver_prompt(
+            branch_name, target_name, repo_path
+        )
+        command = resolver_template.replace(
+            '{prompt}', shlex.quote(prompt)
+        )
+
+        env = os.environ.copy()
+        env['GITUP_BRANCH'] = branch_name
+        env['GITUP_TARGET'] = target_name
+        env['GITUP_REPO_PATH'] = repo_path
+
+        result = subprocess.run(
+            command, shell=True, cwd=repo_path, env=env
+        )
+
+        if result.returncode != 0:
+            raise UnresolvedConflictError(
+                branch_name, target_name, repo_path
+            )
+
+        # Verify rebase completed
+        git_dir = subprocess.run(
+            ['git', 'rev-parse', '--git-dir'],
+            cwd=repo_path, capture_output=True, text=True
+        ).stdout.strip()
+
+        if not os.path.isabs(git_dir):
+            git_dir = os.path.join(repo_path, git_dir)
+
+        if (os.path.isdir(os.path.join(git_dir, 'rebase-merge')) or
+                os.path.isdir(os.path.join(git_dir, 'rebase-apply'))):
+            raise UnresolvedConflictError(
+                branch_name, target_name, repo_path
+            )
+
+        print(colored('conflict resolved', 'green'))
+        return True
+
     def fetch(self):
         """
         Fetch the recent refs from the remotes.
diff --git a/PyGitUp/tests/test_conflict_resolver.py b/PyGitUp/tests/test_conflict_resolver.py
new file mode 100644
index 0000000..cad67ff
--- /dev/null
+++ b/PyGitUp/tests/test_conflict_resolver.py
@@ -0,0 +1,129 @@
+# System imports
+import os
+import stat
+from os.path import join
+
+import pytest
+from git import *
+from PyGitUp.git_wrapper import RebaseError, UnresolvedConflictError
+from PyGitUp.tests import basepath, write_file, init_master, update_file, \
+    testfile_name
+
+test_name_success = 'conflict_resolve_success'
+test_name_fail = 'conflict_resolve_fail'
+test_name_noresolver = 'conflict_no_resolver'
+
+repo_path_success = join(basepath, test_name_success + os.sep)
+repo_path_fail = join(basepath, test_name_fail + os.sep)
+repo_path_noresolver = join(basepath, test_name_noresolver + os.sep)
+
+
+def setup_conflict_repo(test_name):
+    """Set up a repo with a rebase conflict."""
+    master_path, master = init_master(test_name)
+
+    # Prepare master repo
+    master.git.checkout(b=test_name)
+
+    # Clone to test repo
+    path = join(basepath, test_name)
+    master.clone(path, b=test_name)
+    repo = Repo(path, odbt=GitCmdObjectDB)
+    assert repo.working_dir == path
+
+    # Modify file in master
+    update_file(master, test_name)
+
+    # Modify same file in our repo (conflicting change)
+    contents = 'completely changed!'
+    repo_file = join(path, testfile_name)
+    write_file(repo_file, contents)
+    repo.index.add([repo_file])
+    repo.index.commit(test_name)
+
+    # Modify file in master again
+    update_file(master, test_name)
+
+    return master, repo
+
+
+def make_resolver_script(basedir, script_content):
+    """Write a resolver shell script and return its path."""
+    script_path = join(basedir, 'resolver.sh')
+    write_file(script_path, script_content)
+    os.chmod(script_path, stat.S_IRWXU)
+    return script_path
+
+
+def setup_module():
+    global master_success, repo_success
+    global master_fail, repo_fail
+    global master_noresolver, repo_noresolver
+
+    master_success, repo_success = setup_conflict_repo(test_name_success)
+    master_fail, repo_fail = setup_conflict_repo(test_name_fail)
+    master_noresolver, repo_noresolver = setup_conflict_repo(
+        test_name_noresolver
+    )
+
+
+def test_resolver_succeeds():
+    """Resolver fixes conflicts and completes rebase."""
+    os.chdir(repo_path_success)
+
+    script = make_resolver_script(repo_path_success, (
+        '#!/bin/bash\n'
+        'git checkout --theirs .\n'
+        'git add -A\n'
+        'GIT_EDITOR=true git rebase --continue\n'
+    ))
+
+    from PyGitUp.gitup import GitUp
+    gitup = GitUp(testing=True)
+    gitup.settings['rebase.conflict-resolver'] = script + ' {prompt}'
+    gitup.run()
+
+    assert 'rebasing' in gitup.states
+
+
+def test_resolver_fails():
+    """Resolver exits non-zero; UnresolvedConflictError is raised."""
+    os.chdir(repo_path_fail)
+
+    script = make_resolver_script(repo_path_fail, (
+        '#!/bin/bash\n'
+        'exit 1\n'
+    ))
+
+    from PyGitUp.gitup import GitUp
+    gitup = GitUp(testing=True)
+    gitup.settings['rebase.conflict-resolver'] = script + ' {prompt}'
+
+    with pytest.raises(UnresolvedConflictError):
+        gitup.run()
+
+
+def test_no_resolver():
+    """Without a resolver, RebaseError is raised as before."""
+    os.chdir(repo_path_noresolver)
+
+    from PyGitUp.gitup import GitUp
+    gitup = GitUp(testing=True)
+
+    with pytest.raises(RebaseError):
+        gitup.run()
+
+
+def test_prompt_content():
+    """Prompt includes branch name, target, and instructions."""
+    from PyGitUp.gitup import GitUp
+    os.chdir(repo_path_success)
+
+    gitup = GitUp(testing=True)
+    prompt = gitup._build_resolver_prompt(
+        'my-branch', 'origin/main', repo_path_success
+    )
+
+    assert 'my-branch' in prompt
+    assert 'origin/main' in prompt
+    assert 'Resolve the git rebase conflicts' in prompt
diff --git a/README.rst b/README.rst
index 859fd75..c419f72 100644
--- a/README.rst
+++ b/README.rst
@@ -143,6 +143,30 @@ options:
   ``PyGitUp`` will show the hashes of the current commit (or the point
   where the rebase starts) and the target commit like ``git pull`` does.
 
+-  ``git-up.rebase.conflict-resolver [cmd]``: If set, ``PyGitUp`` will
+   invoke this command when a rebase conflict occurs. The command should
+   contain a ``{prompt}`` placeholder, which will be replaced with a
+   shell-escaped prompt containing conflict context (branch names,
+   conflicted files, and resolution steps). The command is expected to
+   resolve all conflicts, stage the files, and run
+   ``git rebase --continue``. If it exits with code 0 and the rebase is
+   complete, ``git up`` continues to the next branch. If it fails, the
+   repo is left in the conflicted state for manual resolution.
+
+   Environment variables ``GITUP_BRANCH``, ``GITUP_TARGET``, and
+   ``GITUP_REPO_PATH`` are also set for the resolver process.
+
+   Examples::
+
+     git config git-up.rebase.conflict-resolver "claude -p {prompt}"
+     git config git-up.rebase.conflict-resolver "claude -p {prompt} --dangerously-skip-permissions"
+     git config git-up.rebase.conflict-resolver "aider --message {prompt}"
+
+   Note: AI agents like ``claude`` may prompt for tool approvals by
+   default. Use ``--dangerously-skip-permissions`` to run fully
+   autonomously, or ``--allowedTools 'Edit,Read,Bash,Write,Glob,Grep'``
+   to scope the permissions.
+
 New in v1.0.0:
 ~~~~~~~~~~~~~~