This study investigates the three speech act strategies of request, suggestion and apology in Libyan Arab EFL undergraduate students (AREFLUS) and Amazigh EFL undergraduate students (AMEFLUS). It also examines their linguistic and pragmatic competence in these strategies. Two Libyan universities (Sebha and Zwara) are selected for the study, which includes 50 AREFLUS and 37 AMEFLUS participants. To investigate the students' socio-pragmatic and pragma linguistic competence, two instruments are used: a questionnaire in the form of a Discourse Completion Test (DCT) and a rating scale. The results reveal numerous similarities between the Libyan Arab and Amazigh participants in performing all the speech act strategies of request, suggest and apology. However, some significant differences regarding gender are found among Libyan EFL students. Overall, both groups appear to be more competent in functioning than in structuring the three mentioned speech act strategies.