We propose and investigate a paradigm for activity recognition, distinguishing the ‘on-going activity’ recognition task (OGA) from that addressing ‘complete activities’ (CA). The former starts from a time interval and aims to discover which activities are going on inside it. The latter, in turn, focuses on terminated activities, and amounts to taking an external perspective on activities. We argue that this distinction is quite natural and that the OGA task has a number of interesting properties; e.g., the possibility of reconstructing complete activities in terms of on-going ones, the avoidance of the thorny issue of activity segmentation and a straightforward accommodation of complex activities, etc. Moreover, some plausible properties of the OGA task are discussed and then investigated in a classification study, addressing: the dependence of classification performance on the duration of time windows and its relationship with actional types (homogeneous vs. non-homogeneous a...