Two experiments are presented that test the predictions of two associative learning models of Artificial Grammar Learning. The two models are the simple recurrent network (SRN) and the competitive chunking (CC) model. The two experiments investigate acquisition of different types of knowledge in this task: knowledge of frequency and novelty of stimulus fragments (Experiment 1) and knowledge of letter positions, of small fragments, and of large fragments up to entire strings (Experiment 2). The results show that participants acquired all types of knowledge. Simulation studies demonstrate that the CC model explains the acquisition of all types of fragment knowledge but fails to account for the acquisition of positional knowledge. The SRN model, by contrast, accounts for the entire pattern of results found in the two experiments.