An efficient procedure for derivation of mean outcrossing rates for non-linear wave-induced responses in stationary sea states is presented and applied to an analysis of the horizontal deck sway of a jack-up unit. The procedure is based on the theory of random vibrations and uses the first order reliability method (FORM) to estimate the most probable set of wave components in the ocean wave system that will lead to exceedance of a specific response level together with the associated mean outcrossing rate. The procedure bears some resemblance to the Constrained NewWave methodology, but is conceptually simpler and makes efficient use of the optimisation procedures implemented in standard FORM software codes. Due to the fast calculation procedure the analysis can be carried out taking into account all relevant non-linear effects. Specifically, the present analysis accounts for second order stochas-tic waves, not previously included in the analysis of jack-up units in stochastic seaways.