A novel nonlinear control algorithm based on hybrid neural networks is presented to cope with the high-accuracy synchronization control problem for a dual-actuator electrohydraulic drive system which plays an important role for the development of elastomeric launchers. A new objective function for better synchronization performance is introduced and a learning algorithm to adjust the weights of the neural network, based on the gradient descent algorithm, is also derived. The hybrid neural network control algorithm guarantees high-accuracy synchronization performance of two motion cylinders and fast dynamic response as well as good stability of the control system. Prototype test results on the dual-actuator electrohydraulic drive system verifys the effectiveness of the proposed approach.