Performing data mining tasks in streaming data is considered a challenging research direction, due to the continuous data evolution. In this work, we focus on the problem of clustering streaming time series, based on the sliding window paradigm. More specifically, we use the concept of ?-clusters in each time instance separately. A subspace ?- cluster consists of a set of streams, whose value difference is less than ? in a consecutive number of time instances (dimensions). The clusters can be continuously and incrementally updated as the streaming time series evolve. The proposed technique is based on a careful examination of pair-wise stream similarities for a subset of dimensions and then, it is generalized for more streams per cluster. Performance evaluation results show that the proposed pruning criteria are important for search space reduction, and that the cost of incremental cluster monitoring is computationally more efficient than reclustering.