The author provides a definition and some theoretical and experimental-diagnostical bases for a study of the extra-normative activity of an individual or a collective presented as a manifestation of their active civic position. Extranormative activity is defined as correspondence of acts, attitudes, and results of a practical activity of the social subject (a collective or an individual) to moral expectations which though can not be required of him as something he is obliged to perform (officially prescribed, legislated, and - in that sense - normative), but still satisfy certain interests (goals, ideals, values) of the society for the sake of which this activity is being performed. A "working" scheme of basic psychological manifestations of the extranormative activity is suggested, as well as some lines of experimental-diagnostical study of it. The notion of extra-normative activity is correlated with those of responsibility and social activity.