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In this paper a nonholonomic mobile robot with completely unknown dynamics is considered. An efficient single layered neural network controller is assumed for the real time path tracking control of the mobile robot. The controller takes advantage of the robot regressor dynamics that express the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. The influence of time delays in the input control torque on the stability of the mobile robot motion has been studied. The present work enables to estimate the maximum admissible time delay in the input control torque with out the loss of stability in robot motion and guaranteed tracking performance.