∗Supported in part by NSF under grants IRI-96-25901 and 0090145. †Supported in part by grants from NSF, ONR, AFOSR, and MICRO. We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent’s initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.