In this paper, generalized forms of amplitude and intensity K-distributions are proposed to model multi-look synthetic aperture radar (SAR) data. The approach is based upon a product model in which the amplitude and intensity distributions of the SAR backscatter component are assumed to be Laguerre orthogonal expansions of the traditional clutter distribution. The SAR intensity and amplitude probability density functions (pdfs) are derived and turn out to be the weighted combination of a series of K-distributions. Several theoretical and implementation issues regarding the proposed generalization are discussed. Comparative experimental results using real SAR data indicates that these generalized forms of K may allow better estimation of the SAR pdf than that of the “traditional” K distribution.