The problem of mutual collisions of manipulators of a dual-arm multi-link robot (so-called self-collisions) arises during the performance of a cooperative technological operation. Self-collisions can lead to non-fulfillment of the technological operation or even to the failure of the manipulators. In this regard, it is necessary to develop a method for online detection and avoidance of self-collisions of manipulators. The article presents a method for detecting and avoiding self-collisions of multi-link manipulators using an artificial neural network by the example of the dual-arm robot SAR-401. A comparative analysis is carried out and the architecture of an artificial neural network for self-collisions avoidance control of dual-arm robot manipulators is proposed. The novelty of the proposed approach lies in the fact that it is an alternative to the generally accepted methods of detecting self-collisions based on the numerical solution of inverse kinematics problems for manipulators in the form of nonlinear optimization problems. Experimental results performed based on MATLAB model, the simulator of the robot SAR-401 and on the real robot itself confirmed the applicability and effectiveness of the proposed approach. It is shown that the detection of possible self-collisions using the proposed method based on an artificial neural network is performed approximately 10 times faster than approaches based on the numerical solution of the inverse kinematics problem while maintaining the specified accuracy.