Large language models (LLMs) deployed as conversational agents are increasingly expected to follow procedural logic. While factual hallucination has received extensive attention, a different failure mode has been overlooked: procedural hallucination, in which an agent produces individually fluent and factually plausible utterances while deviating from the intended conversational process. We introduce DialFork, the first benchmark to measure this failure mode on raw dialogue text. DialFork is built by forking conformant dialogues at controlled turn positions and injecting one of four hallucination types, yielding 36,278 dialogues across 24 tasks in 12 domains; 30 human annotators validate the construction. We define three evaluation tasks that characterize procedural deviation at three granularities: how far a set of dialogues deviates from conformant ones (monitoring deployed agents), how far a single dialogue does (procedural retrieval), and at which turn a dialogue first goes off-track (real-time guardrails). For the first two, we propose dialog-flow-aware metrics, FlowKL and FlowScore, that compare dialogues by how they unfold rather than their content. At the dialogue level, FlowScore significantly outperforms all baselines across seven encoders, showing that semantic similarity is no substitute for procedural similarity. We release DialFork under the MIT license at https://github.com/idiap/dialfork, hoping the community will measure conversational process alongside content.