This chapter considers cooperative kinematic control of multiple robot arms with a full distributed control topology by using distributed recurrent neural networks. The problem is formulated as a constrained game, where energy consumptions for each robot arm, saturations of control input, and the topological constraints imposed by the communication graph are taken into account. An implicit form of the Nash equilibrium for the game is obtained by converting the problem into its dual space. Then, a distributed dynamic controller based on recurrent neural networks is devised to drive the system towards the desired Nash equilibrium to seek the optimal solution of the cooperative control. Global stability and solution optimality of the neural networks are proved in theory. Simulations demonstrate the effectiveness of the method presented in this chapter.