Most existing works on detection of social groups or communities in online social networks consider only the common topical interest of users as the basis for grouping. The temporal evolution of user activities and interests have not been thoroughly studied to identify their effects on the formation of groups. In this paper, we investigate the problem of discovering and tracking time-sensitive activity driven user groups in dynamic social networks. The users in these groups have the tendency to be temporally similar in terms of their activities on the topics of interest. To this end, we develop two baseline solutions to discover effective social groups. The first solution uses the network structure, whereas the second one uses the topics of common interest. We further propose an index-based method to incrementally track the evolution of groups with a lower computational cost. Our main idea is based on the observation that the degree of user activeness often degrades or upgrades widely over a period of time. The temporal tendency of user activities is modelled as the freshness of recent activities by tracking the social streams with a fading time window. We conduct extensive experiments on two real data sets to demonstrate the effectiveness and performance of the proposed methods. We also report some interesting observations on the temporal evolution of the discovered social groups.