Individuals with agrammatic Broca's aphasia experience difficulty when processing reversible non-canonical sentences. Different accounts have been proposed to explain this phenomenon. The Trace Deletion account (Grodzinsky, 1995, 2000, 2006) attributes this deficit to an impairment in syntactic representations, whereas others (e.g., Caplan, Waters, Dede, Michaud, & Reddy, 2007; Haarmann, Just, & Carpenter, 1997) propose that the underlying structural representations are unimpaired, but sentence comprehension is affected by processing deficits, such as slow lexical activation, reduction in memory resources, slowed processing and/or intermittent deficiency, among others. We test the claims of two processing accounts, slowed processing and intermittent deficiency, and two versions of the Trace Deletion Hypothesis (TDH), in a computational framework for sentence processing (Lewis & Vasishth, 2005) implemented in ACT-R (Anderson, Byrne, Douglass, Lebiere, & Qin, 2004). The assumption of slowed processing is operationalized as slow procedural memory, so that each processing action is performed slower than normal, and intermittent deficiency as extra noise in the procedural memory, so that the parsing steps are more noisy than normal. We operationalize the TDH as an absence of trace information in the parse tree. To test the predictions of the models implementing these theories, we use the data from a German sentence-picture matching study reported in Hanne, Sekerina, Vasishth, Burchert, and De Bleser (2011). The data consist of offline (sentence-picture matching accuracies and response times) and online (eye fixation proportions) measures. From among the models considered, the model assuming that both slowed processing and intermittent deficiency are present emerges as the best model of sentence processing difficulty in aphasia. The modeling of individual differences suggests that, if we assume that patients have both slowed processing and intermittent deficiency, they have them in differing degrees.