Because of the predominance of large emittances, muon storage rings have a tendency to being rather sensitive to nonlinear effects. In this paper we study the effects of the nonlinearities due to the lattice elements’ fringe fields, which have a fundamentally different behavior from normal multipole terms. It is found that for given scenarios for lattices and emittances, the fringe field effects have dramatic influences on the dynamics and stability of particles and hence require careful study of correction options. ©2000 American Institute of Physics.