A theory for multi-pump and multi-motor hydraulic systems is presented in this paper based on the analysis of the advantages and disadvantages of the popular hydraulic transmission and the double-stator motor(pump).By taking the single-acting fixed displacement multi-pump and multi-motor driving system as an example,the output speeds in a variety of connections of this novel hydraulic transmission are analyzed theoretically.This research work lays a theoretical foundation for the study of the multi-pump and multi-motor driving system and for the design of the system principle diagram. A theory for multi-pump and multi-motor hydraulic systems is presented in this paper based on the analysis of the advantages and disadvantages of the popular hydraulic transmission and the double-stator motor (pump) .By taking the single-acting fixed displacement multi -pump and multi-motor driving system as an example, the output speeds in a variety of connections of this novel hydraulic transmission are analyzed theoretically. This research work lays a theoretical foundation for the study of the multi-pump and multi-motor driving system and for the design of the system principle diagram.