In a recent paper (Hairer-Wanner [1]) we have given a theory with which it is easy to calculate the order conditions for Nyström methods. Here we show how it is possible to solve this system of non-linear algebraic equations. Moreover we present all methods of orders for s=2, 3, 4 (s-1 indicates the number of function evaluations per step); methods with one parameter of orders for s=5, 6 and some special methods of order s-1 for s=8, 9.