This study investigated the relationship between L1 and the developmental sequences for the acquisition of temporal morphology that are predicted by the aspect hypothesis. The use of tense-aspect markers in 7,784 past contexts by 139 Japanese-and French-speaking ESL learners was analyzed. A repeated measures ANOVA supported the predictions of the aspect hypothesis. For both L1 groups, the marking of past spread from achievements and accomplishments (telics) through activities to statives, and the preferred non-past responses for statives and activities were present and progressive, respectively. The magnitude, rather than the direction, of the lexical aspect effect with achievements was the only significant L1 difference. The results lend support to the hypothesis that the influence of lexical aspect on the acquisition of grammatical morphology is a language learning universal. They are also consistent with research on other linguistic features in which selective influence of L1 on developmental sequences has been observed.