Is mapping a necessary condition for analogical transfer ? According to classical models of reasoning by analogy (SME, AcME, SIAM, IAM), analogical transfer requires that subjects make first of all complete one-to-one correspondences between base and target elements. It is only when the mapping is finished that subjects may project inferences from the base to the target. Consequently, these models predict that a cross-mapping between base and target (same base-target elements which play different roles) should increase the time necessary for transfering a property from the base to the target: Empirical results obtained here are inconsistent with this prediction because, in a series of experiments, we show that the increase in time to match two cross-mapping objects does not involve an increase in time to process the target. Consequently, it seems that there is at least a partial independency between mapping and transfer.