The aim of the present study was to examine science and non-science education secondary school teachers' skill to evaluate arguments, and how this skill relates to their skill to construct arguments and to their perceptions about their ability to teach argumentation skills effectively. The study also examined whether teachers' argument skills and their self-efficacy of teaching argumentation were domain-specific. Social-science education teachers, who teach literature and history, and physical science education teachers, were asked to write two essays -- one on a social topic and another on a socio-scientific topic--, to evaluate the quality of written arguments and to complete an instrument assessing their self-efficacy of teaching argumentation. Results showed that teachers' ability to construct arguments predicted their ability to evaluate arguments. Yet, although teachers expressed high self-efficacy in teaching argumentation in both domains, their abilities to evaluate and construct arguments were not sufficiently developed, in neither domain. The findings of the present study have important educational implications, suggesting that specific attention needs to be paid on teachers' skills of constructing and evaluating arguments.