This paper discusses the supervised learning of morphology using stochastic transducers, trained using the ExpectationMaximization (EM) algorithm. Two approaches are presented: first, using the transducers directly to model the process, and secondly using them to define a similarity measure, related to the Fisher kernel method (Jaakkola and Haussler, 1998), and then using a Memory-Based Learning (MBL) technique. These are evaluated and compared on data sets from English, German, Slovene and Arabic. .