In this thesis a method is developed to solve the problem of path planning for two 2R type robots, which share workspace and thus present dynamic obstacle to each other. This problem, according to its computational complexity, belongs to NP complete class problems. Solving such problems with exact mathematical algorithms with known upper time complexity bound is limitedly applicable. The motion planning methodology developed in this thesis is based on concurrent path planning of both robots using parallel, partly independent evolutionary – coevolutionary algorithms. Time efficient planning is possible for two robots using developed algorithms what proves the hypothesis formulated in the dissertation. To prove the hypothesis, a simulation environment is developed in the first step, in which path planning is possible for arbitrary setup of initial and final configurations of the robots. It is possible to conduct path planning either for one robotic agent or for more, including presence of arbitrarily distributed obstacles. Set of criteria is determined to evaluate the evolution of agents, and the nature of connections between different conflicting criteria is revealed. Number of collisions, total path, joint rotation angle and velocity profile of the end effector are the criteria to be optimized. Formal analysis of the system composed of two 2R type robots is conducted and analytical conditions for collision occurrence are derived. Based on these understandings, the fitness function is formulated with appropriate selection mechanisms, what enabled parallel evolution and adaptation between the two robotic agents. The result is continuous, time and energy efficient motion without collisions for the two agents in the given workspace. To additionally optimize processing time; a motion discretization method is proposed together with complementary motion reconstruction method to execute the motion with arbitrarily small time step between two consecutive configurations. The methodology proposed in this thesis is verified on a real robotic system composed of two robots for which the path planning problem is successfully solved.