Abstract: In distributed data stream systems, the available communication bandwidth is a bottleneck In order to reduce the communication overhead under the constraint of the precision of the answers to queries, a new method for transferring data streams, named compound data streams, is proposed The idea is that raw data streams are grouped and merged into compound data streams which are then transferred instead of the raw data streams Based on the definition of compound data streams, the generation algorithm of compound data streams is given Meanwhile, the error of the answers to queries and issues related to compound data streams are studied The experimental results show that the proposed method is very efficient