Since the beginning of the Nineteen-eighties, cognitive scientists have shown increasing interest in a range of phenomena, processes and capacities underlying human interaction, collectively referred to as intersubjectivity. The goal of this line of research is to give an account of the various forms of human interaction, and in particular of the affective, attentional and intentional determinants of joint activity. The main thesis we develop in the paper is that so far the authors interested in intersubjectivity have neglected, or at least undervalued, an important aspect of joint activity, that is, the essentially normative character of collective intentionality. Our approach to joint activity is mainly based on Margaret Gilbert's theory of plural subjects. Gilbert's general idea is that joint activities should be regarded as activities carried out by individuals who stand to one another in a special relation, called joint commitment, which has an intrinsically normative nature. As we shall try to show, the concept of a joint commitment is a powerful tool to explain certain specific features of joint activities. In the paper we first point out certain explanatory inadequacies of the current models of intersubjectivity, and contend that such inadequacies depend on failing to appreciate the fundamental role of normativity in collective intentionality. We briefly sketch Gilbert's theory of plural subjects, and introduce the concept of a joint commitment, and then discuss some lines along which a psychology of plural subjects may be developed.