Existing data stream models commonly assume that users' records or profiles in data streams will not be updated once they arrive. In many applications such as web usage, however, the users' records/profiles may evolve along time. This kind of streaming transactions are referred to as bi-streaming data - the data evolves temporally in two dimensions, the flowing of transactions as with the traditional data streams, and the evolving of users' profiles inside the streams, which makes bi-streaming data different from traditional data streams. The two-dimensional evolving of bi-streaming data brings difficulties on modeling and clustering for exploring the users' behaviours. This paper will propose three models to summarize bi-streaming data, which are the batch model, the Evolving Objects (EO) model and the Dynamic Data Stream (DDS) model. Through creating, updating and deleting user profiles, the models summarize the behaviours of each user as an object. Based on these models, clustering algorithms are employed to identify the user groups. The proposed models are tested on a real-world data set showing that the DDS model can summarize the bi-streaming data efficiently and effectively, providing better basis for clustering user profiles than the other two models.