The dissertation concerns the acquisition of a second language (L2) by adults, mainly aiming at uncovering the factors that determine its course of development. Within the framework of a research tradition established in the 1990s, it is assumed that these determinants can be most effectively revealed through systematic comparison with the course of first language (L1) acquisition. Similarities and differences between the two developmental processes are sought in order to pinpoint factors that differentiate them. The study focuses upon the development of the ability to construct narratives in Greek, which are elicited on the basis of a silent animated film. It investigates the temporal structure of narratives, more specifically the means used (e.g. lexical and grammatical like adverbs, aspect and aktionsart) for marking temporal sequence as well as simultaneity of events. A cross-sectional sample of eight groups of participants is used: children aged four, seven and ten as well as adults speaking Greek as an L1 and Albanian L1 learners of Greek as an L2 at beginner, intermediate and advanced levels. Ιn order to detect language transfer, a limited number of participants narrated in their native Albanian language. Results show marking of temporal sequence of events preceding that of simultaneity in both L1 and L2 acquisition. In L1 acquisition children's first attempts to mark both temporal relations are problematic. Children prefer explicit marking of these temporal relations at first, i.e. perfective aspect (in past tense) and adverbs for temporal sequence as well as temporal clauses for simultaneity. Adults, however, rely equally on actionsart (in present tense) to forward narrative time and conversational implicatures to suggest simultaneity. However, in L2 acquisition, the developmental course differs. Beginners rely upon actionsart to move narrative time, intermediate level speakers mainly upon past perfective verb forms and adverbs, while both ways are used at advanced level. Temporal simultaneity is marked through a variety of means, but often ineffectively until advanced level of language proficiency. The comparison of L1 and L2 acquisition shows that differences in cognitive and linguistic/communicative background in early levels of development lead to different types of narratives as a result of different levels of discourse skills. Adult L2 learners construct temporally coherent narratives even at the beginner level. By contrast, children at an early age fail to construct narratives with a temporal structure, despite their comparatively more advanced lexical and grammatical skills. However, despite differences in L1 and L2 learners' background, some similarities in discourse structure were observed, such as a tendency for linear temporal organization and past tense anchoring of narratives at intermediate level of proficiency.