The study addresses the cyclically temporal aspect of sequence recognition, storage and recall using the Recurrent Oscillatory Self-Organizing Map (ROSOM), first introduced by Kaipainen, Papadopoulos and Karhu (1997). The unique solution of the network is that oscillatory States are assigned to network units, corresponding to their `readiness-to-fire'. The ROSOM is a categorizer, a temporal sequence storage system and a periodicity detector designed for use in an ambiguous cyclically repetitive environment. As its external input, the model accepts a multidimensional stream of environment-describing feature configurations with implicit periodicities. The output of the model is one or a few closed cycles abstracted from such a stream, mapped as trajectories on a two-dimensional sheet with an organization reminiscent of multi-dimensional scaling. The model's capabilities are explored with a variety of workbench data.