- A new method for predicting slowly-varying wave drift excitations in multidirectional seas is developed and compared to existing methods based on index and envelope approximations. The present method retains the assumption of narrow bandedness in frequency but treats the wave directional spreading exactly. The method is consequently more applicable for realistic seas but is comparable in computational effort to the other techniques. For the interesting case when storm and swell seas are present from different directions, surprising new results are obtained which indicate that the slowly-varying forces on an axisymmetric body can be greatly amplified when the wave systems are incident from opposing directions. For each of the methods, the slowly-varying force spectra are derived and their statistics confirmed against time-history simulations. For the index and envelope approximations, theoretical probability distributions of the slowly-varying force are reexamined and generalized, and compared satisfactorily to numerically simulated histograms. 1989.