This paper describes the use of the Monte Carlo code MCNPX-PoliMi for nuclear-nonproliferation applications, with particular emphasis on the simulation of spontaneous and neutron-induced nuclear fission. New models for the outgoing neutrons and gamma rays emitted in spontaneous and induced fission are described. For spontaneous fission, the models include prompt neutron energy distributions that depend on the number of neutrons emitted in the individual fission events. For neutron-induced fission, due to lack of data, the prompt neutron energy distributions are independent of the number of neutrons emitted in the individual fission events. Gamma rays are sampled independently of the neutrons. Code validation is performed on well-characterized mixed-oxide fuel and plutonium-oxide samples.