Abstract: Abstract: This paper studied the speed ratio control problem of the hydraulic mechanical continuously variable transmission. First, based on the speed ratio characteristics of the transmission and the experiment on the identification of the hydraulic system, the steady-state and dynamic mathematical model among the excitation current of the variable displacement pump, the speed ratio of the pump-motor system and the speed ratio of the transmission were built. It showed that the speed ratio of the transmission is a segmented function of the speed ratio of pump-motor system. The relationship between the excitation current of the variable displacement pump and the speed ratio of pump-motor can be considered as a third-order system. According to this model, a neural PID controller based on single neuron network was developed. A set of feasible parameters, i.e. the inertia coeffecient k and the learning coeffecient ηP, ηI, ηD of the PID controller can be determined according to the tuning law which have been studied based on the simulation and experiment. From that, it showed that an appropriate k, ηP, a larger ηI and a smaller ηD can meet a satisfactory internal-stage control quality. Secondly, the open-loop and closed-loop control mode defined by a relay logic was proposed in this paper, so as to make the neural PID controller work at specific intervals and conditions and effectively avoid the frequently power-shift and direction-changed of motor rotation. The controller calculates the target stage and direction of motor rotation according to the target speed ratio of transmission. Once the current stage and direction of motor rotation are different from the target, the power-shift logic and the displacement adjustment logic of the pump can be actived by the open-loop controller to reach the target states following the stepless speed changing rule, otherwise, the closed-loop controller would adjust the speed ratio of the transmission to the target without power-shift and direction-changed of motor rotation based on the neural PID technology. Finally, an experiment of speed ratio control was conducted. During the experiment, it took 5-6 s to hold one direction of motor rotation when the open-loop controller worked, the process under the speed ratio control was smooth and steady and no steady-state error was there at the end of the experiment, the results proved the algorithm to be correct and feasible.