Abstract: Authors present a modified combined search method for solving the inverse problem of the kinematics of a multi-link manipulator under conditions of target motion. A genetic algorithm was used for the initial approximation to the goal and simplex search to improve the results of the genetic algorithm. Compensation of the effect of the movement of the target on the objective function is based on estimates of the drift of the target along each axis of the working space. These estimates were used to subtract the contribution of drift to the objective function, which improves search efficiency. The estimates were calculated by the recursive least squares method. Experiments were carried out on mathematical models of planar and spatial, kinematically redundant and non-redundant multi-link manipulators. The results showed that for all the above manipulators it is possible to plan the trajectory according to the position and orientation of the working member, and the constructed trajectories in the generalized coordinates are smooth and do not have abrupt changes. The combined search method finds the solution of the inverse kinematics problem for one iteration of the search procedure due to the global properties of the genetic algorithm and the efficiency of the simplex search.