We propose an ACT-R cue-based retrieval model of the real-time gender predictions displayed by second language (L2) learners. The model extends a previous model of native (L1) speakers according to two central accounts in L2 sentence processing: (i) the Interference Hypothesis, which proposes that retrieval interference is higher in L2 than L1 speakers; (ii) the Lexical Bottleneck Hypothesis, which proposes that problems with gender agreement are due to weak gender representations. We tested the predictions of these accounts using data from two visual world experiments, which found that the gender predictions elicited by German possessive pronouns were delayed and smaller in size in L2 than L1 speakers. The experiments also found a “match effect”, such that when the antecedent and possessee of the pronoun had the same gender, predictions were earlier than when the two genders differed. This match effect was smaller in L2 than L1 speakers. The model implementing the Lexical Bottleneck Hypothesis captured the effects of smaller predictions, smaller match effect and delayed predictions in one of the two conditions. By contrast, the model implementing the Interference Hypothesis captured the smaller prediction effect but it showed an earlier prediction effect and an increased match effect in L2 than L1 speakers. These results provide evidence for the Lexical Bottleneck Hypothesis, and they demonstrate a method for extending computational models of L1 to L2 processing.