Agent Skills are instruction files that tell a coding agent how to do one job. Users install skills from many authors, so two skills for the same job can be active at the same time. We ask what a model does when both skill files are in its context: does it combine their compatible rules, or follow one skill and drop the other? We build SkillClash, 16 pairs of same-job skills in which code checks every rule and a reference output shows the best result that can be reached. On seven models from five families, from 4B open models to Qwen3-235B and GPT-4.1, a skill's rules are followed 93 to 99% of the time when it is loaded alone and 61 to 62% when a same-job skill is loaded next to it. Most outputs show takeover: every rule that only one skill asks for is followed, and every rule that only the other skill asks for is dropped. The worked examples inside the skills drive this. When each skill file instead ends with one example that follows both skills, takeover falls to 1 to 15% on the six models we tested. Telling the model which skill has priority does not bring the dropped skill back, and telling it to apply both skills brings the dropped skill back only on the two strong models and leaves the interacting rules broken. One merged skill file written by the strongest model we used, Claude Opus 5.5, lets all seven models follow 96 to 99% of the achievable rules. Most of its gain over a plain list of both skills' rules comes from its one worked example, and such an example helps only when it is correct. Code and data: https://github.com/prazmara/skillclash

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