A moderate belief-disagreement between agents on proposition p means that one agent believes p and the other agent does not. This paper presents two logical systems, $$\mathbf {MD}$$ and $$\mathbf {MD}^D$$ , that describe moderate belief-disagreement, and shows, using possible worlds semantics, that $$\mathbf {MD}$$ is sound and complete with respect to arbitrary frames, and $$\mathbf {MD}^D$$ is sound and complete with respect to serial frames. Syntactically, the logics are monomodal, but two doxastic accessibility relations are involved in their semantics. The notion of moderate belief-disagreement, which is in accordance with the understanding of belief-disagreement in everyday life, is an epistemic one related to multiagent situations, and $$\mathbf {MD}$$ and $$\mathbf {MD}^D$$ are two epistemic logics.