Floating Production, Storage and Offloading (FPSO) Systems are subjected to stochastic wave loads. In this context, an approach for stochastic fatigue analysis of FPSO topside equipment is developed. Proper FPSO transfer functions, and the Ochi-Hubble sea wave elevation spectrum are combined to provide the design spectrum at the topside of the FPSO. The equipment response is simulated by a time series model; it is approximated as the output of digital filters to a band-limited white noise input. The rainflow cycle counting method is applied to the equipment response time history to identify significant cycles that produce fatigue damage. By using a S-N fatigue life curve, and Miner's linear damage accumulation rule, the fatigue life is estimated for a generic piece of equipment. The results of the rainflow cycle counting method are supplemented by results from a power spectrum based, exclusively, approach.