Several studies have shown selective deficits in the production and comprehension of verb forms referring to the past. On the basis of this evidence the Past Discourse Linking Hypothesis (Bastiaanse et al., 2011) suggests that individuals with aphasia have difficulties with verb forms referring to the past, in comparison to non-past forms such as the present and the future. However, many studies provide counterevidence. This study presents a review of the literature and addresses the question of dissociation between the past and the non-past in aphasia in Greek, a language which distinguishes among three past forms. A mixed group of eight individuals with aphasia and a group of 10 non-brain-damaged speakers performed the two tasks of the Greek version of the Test for Assessing Reference of Time (Bastiaanse, Jonkers, & Thompson, 2008): a sentence completion task (primed by pictures) and a sentence-picture matching task. The sentence completion task tested the present, future and three past tenses: past perfective, past imperfective and present perfect. The sentence-picture matching task tested past perfective, present and future. The production data provide evidence for a deficit in the reference to the past but they also suggest difficulties with the future. Interestingly, a dissociation among the three past tenses tested was found. Above chance performance was found in comprehension across tenses. We consider possible accounts of the data and we discuss the implications of these findings for the Past Discourse Linking Hypothesis.