Add to ORKGOur aim is to solve systems of ordinary differential equations potentially candidate to be stiff, so developed methods must have high stability properties and uniform order of convergence. We focus our attention on multivalue methods [1], which are a generalization of classical methods, such as multistep and Runge-Kutta methods, and we extend the solution smoothly by approximating them though a collocation polynomial. These methods require at each time-step the solution of a non linear system of internal stages, so the computational effort is strictly connected to the nature of this system. We are interested in the construction of methods that allow a reduction of this computational cost, so we propose methods with full matrix [6] and struc...