Two possible iconic models of the acquisition of verb agreement in American Sign Language (ASL) are developed and contrasted with a third, morphological account of the acquisition of this aspect of ASL. Additionally, data from spontaneous conversation of deaf children who have deaf parents are considered to test these three models. An iconic model of the acquisition of ASL assumes that the child is capable of making a direct comparison between the form of a sign and the form (or characteristic motion) of its referent. Furthermore, the ability to make this comparison facilitates comprehension or production of iconic signs. Either mime or spatial analogy may facilitate the acquisition of ASL verb agreement. Alternately, typological features may influence the acquisition of both signed and spoken morphologies. Predictions based on the three models were tested against longitudinal data from two deaf children of deaf parents. The subjects were each videotaped on a monthly basis, and detailed transcriptions were made of all contexts where the grammar of ASL required that a verb agree with the real-world location of an argument. All linguistic contexts which permitted optional agreement with a second argument also were examined. Age at which verb agreement was acquired, use of single-indexing and double-indexing, and the use of citation forms were assessed. The data indicate that the acquisition of verb agreement in ASL is neither early nor error-free. The data strongly support the morphological model: verb agreement was not acquired until after the third year, single-indexing was preferred, and the citation forms of verbs were used inappropriately before verb agreement was acquired. (SW)