LLM-based multi-agent systems (MAS) have exhibited remarkable capabilities in collaborative reasoning and decision-making, yet their interconnected communications introduce new systemic risk: localized hallucinations can propagate along agent communication chain, amplify through interactions, and ultimately trigger cascading failures. Existing countermeasures predominantly follow a post-hoc paradigm, identifying failures only after unsafe behaviors emerge, by which time harmful effects may have already spread throughout the agent network. To tackle this problem, we investigate a complementary pre-hoc approach and propose HalluProp, a Propagation-aware Hallucination inference framework that estimates individual agent failures and emergent system-level hallucination risks before inter-agent interaction. First, we model intrinsic hallucination risks by identifying fine-grained semantic misalignment between agent roles and task queries. We then characterize inter-agent risk propagation by modeling both semantic influence and communication topology. Finally, we integrate these two risks via a differentiable Noisy-OR inference mechanism to derive a systemic diagnosis. Extensive experiments show that HalluProp accurately localizes faulty agents, achieving an average AUROC of 84.6%, while enabling sub-second diagnosis with over $65\times$ speedup over post-hoc methods. By facilitating early intervention through upstream screening, HalluProp effectively complements post-hoc methods, highlighting the potential of pre-hoc risk inference for building more reliable multi-agent systems.

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