diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 3affb7e38c..b1467c2ac9 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -157,6 +157,9 @@ jobs:
     env:
       CI: true
       COVERAGE_PROCESS_START: ./pyproject.toml
+      # We only run the llama_cpp tests on the latest Python as they have been regularly failing in CI with `Fatal Python error: Illegal instruction`:
+      # https://github.com/pydantic/pydantic-ai/actions/runs/19547773220/job/55970947389
+      RUN_LLAMA_CPP_TESTS: ${{ matrix.python-version == '3.13' && matrix.install.name == 'all-extras' }}
     steps:
       - uses: actions/checkout@v4
 
@@ -207,6 +210,7 @@ jobs:
     env:
       CI: true
       COVERAGE_PROCESS_START: ./pyproject.toml
+      RUN_LLAMA_CPP_TESTS: false
     steps:
       - uses: actions/checkout@v4
 
diff --git a/tests/models/test_outlines.py b/tests/models/test_outlines.py
index 3758e3c404..f6f11c36fc 100644
--- a/tests/models/test_outlines.py
+++ b/tests/models/test_outlines.py
@@ -6,6 +6,7 @@
 from __future__ import annotations as _annotations
 
 import json
+import os
 from collections.abc import Callable
 from pathlib import Path
 from typing import Any
@@ -80,8 +81,11 @@
     not transformer_imports_successful(), reason='transformers not available'
 )
 
+# We only run this on the latest Python as the llama_cpp tests have been regularly failing in CI with `Fatal Python error: Illegal instruction`:
+# https://github.com/pydantic/pydantic-ai/actions/runs/19547773220/job/55970947389
 skip_if_llama_cpp_imports_unsuccessful = pytest.mark.skipif(
-    not llama_cpp_imports_successful(), reason='llama_cpp not available'
+    not llama_cpp_imports_successful() or os.getenv('RUN_LLAMA_CPP_TESTS', 'true').lower() == 'false',
+    reason='llama_cpp not available',
 )
 
 skip_if_vllm_imports_unsuccessful = pytest.mark.skipif(not vllm_imports_successful(), reason='vllm not available')