Many classiication algorithms are \passive", in that they assign a class-label to each instance based only on the description given, even if that description is incomplete. In contrast , an active classiier can | at some cost | obtain the values of missing attributes, before deciding upon a class label. The expected utility of using an active classiier depends on both the cost required to obtain the additional attribute values and the penalty incurred if it outputs the wrong classiica-tion. This paper considers the problem of learning near-optimal active classiiers, using a variant of the probably-approximately-correct (PAC) model. After deening the framework | which is perhaps the main contribution of this paper | we describe a situation where this task can be achieved ee-ciently, but then show that the task is often intractable.