Given a symplectic map for an accelerator lattice or sequence of elements, we show how to generate a nonlinearly stable symplectic map that has the same linear terms and the same lowest‐order nonlinear terms as the given map. Techniques are presented for producing stable maps both for the case in which the map is given by a generating function and in the case in which the map is given by a Lie map. © 1995American Institute of Physics