An explicit Runge-Kutta type method for systems of ordinary differential equations with special structure is considered. For partitioned systems a family of explicit methods of order six with just six stages is constructed, which makes them more efficient than classic Runge-Kutta methods of order six. It is shown that second order differential equations, which right-hand side doesn't depend on the first derivative, can be rewritten as the considered partitioned systems. Direct application of the constructed methods to them generates two different families of Runge-Kutta-Nyström methods. The comparison of constructed methods with known methods of order six is held.