We study stability in matching markets with two-sided incomplete information. When a blocking opportunity arises, potential deviators draw inferences about one another’s types and iteratively refine their probabilistic beliefs. We first introduce a notion of stability based only on iterative reasoning about rational blocking behavior in the absence of communication. We then develop a refinement that allows for self-enforcing blocking agreements. Intuitively, an agreement is self-enforcing if, when agents believe in the agreement, the resulting inference process leads to behavior that validates it. We discuss the relationship between these two notions of stability and their implications for matching under incomplete information.