We investigated a series of novel motors and pumps with a new structure called double-stator. Double-stator can be used as pump or motor just for the working condition on demand. A certain amount of pumps or motors are formed in one shell and these subpumps or submotors can work alone or in company without influence on other pumps or moters. This kind of double-stator pumps (motors) are called multi-pumps (multi-motors). Through the analysis of multifarious connection modes of single-acting double-stator multi-pumps and multi-motors, the mathematical expressions of output flow rate, rotational speed and torque are acquired. The results indicate that different flow rates can be provided by one fixed displacement double-stator multi-pump system under the condition of an unalterable driven speed. Likewise, under the terms of a fixed input flow and without complex variable mechanisms, the functions of double speeds, multiple speeds and even differential connection can be realized by a double-stator multi-motor system with various output rotational speeds and torques.