Multivariate polynomial approximations are considered to the coupled nonlinear mooring forces acting on a vessel moored with multileg moorings. The objective is to yield explicit forms of equations of the low-frequency vessel motions, since the exact mooring forces are known numerically only. Such forms could then be used for analytical solutions of the equations of motion. It is shown that the polynomials lack sufficient generality and accuracy for this purpose, and hence solution of the problem can be considered only by the exact method.