The problem of finding an admissible object trajectory for a cooperating two-robot system is investigated. The method is based on reformulating the problem as a nonlinear optimization problem with equality constraints in terms of the joint variables. The optimization problem is then solved numerically on a computer. The solution automatically gives the corresponding joint variable trajectories as well, thus eliminating the need for solving the inverse kinematic problem. The performance indices are chose in joint and cartesian spaces and computer simulations are performed.