The work of Longuet-Higgins (1963), on the effects of wave nonlinearity on the statistics of the sea surface, is extended here to obtain the joint distribution of surface elevation and slopes for a nonlinear random sea. The results are used to examine the effect of wave nonlinearity on the form of a radar altimeter pulse which is reflected from the sea surface. It is shown how wave information may be derived from the return pulse and how this can be used to correct errors in the altimeter mean sea level estimate (a problem known as ''sea state bias'').