A probability density function, p(a), for the instantaneous amplitude of the backscattered field at moderate incidence angles is proposed. The key step is in writing the (slowly varying) backscatter cross section, &sgr;0, as an exponential function to second order in the long wave slope component, sx, along the scatterometer look direction; that is, &sgr;0~exp (a1sx+a2s2x). The function p(&sgr;0) is then computed by a straightforward transformation of the normally distributed slope component, while p(a) follows from Bayes' theorem assuming p(a ‖ &sgr;0) to be Rayleigh distributed. The proposed probability density function was compared to Ku band dual-polarized data taken at 20¿ and 45¿ incidence during the Synthetic Aperture and X Band Ocean Nonlinearities experiments at the Chesapeake Light Tower and at Forschungsplatform Nordsee. The function p(a) was found to follow a Weibull distribution with slope parameter &ngr;≂1.9 for small amplitudes. At large amplitudes the distribution lengthens but appears to be neither Weibull nor K distributed as has been reported for near-grazing incidence data. ¿ American Geophysical Union 1994