To have learned the morphology of a natural language is to have the capacity both to recognize and to produce words consisting of novel combinations of familiar morphemes. Most recent work on the acquisition of morphology takes the perspective of production, but it is receptive morphology which comes first in the child. This paper presents a connectionist model of the acquisition of the capacity to recognize morphologically complex words. The model takes sequences of phonetic segments as inputs and maps them onto output units representing the meanings of lexical and grammatical morphemes. It consists of a simple recurrent network with separate hidden-layer modules for the tasks of recognizing the root and the grammatical morphemes of the input word. Experiments with artificial language stimuli demonstrate that the model generalizes to novel words for morphological rules of all but one of the major types found in natural languages and that a version of the network with unassigned hidden-layer modules can learn to assign them to the output recognition tasks in an efficient manner. I also argue that for rules involving reduplication, that is, the copying of portions of a root, the network requires separate recurrent subnetworks for sequences of larger units such as syllables. The network can learn to develop its own syllable representations which not only support the recognition of reduplication but also provide the basis for learning to produce, as well as recognize, morphologically complex words. The model makes many detailed predictions about the learning difficulty of particular morphological rules.