Speckle appearing in synthetic aperture radar (SAR) images is generated by coherent interference of radar echoes from target scatters. Basically, speckle noise has the nature of a multiplicative noise. In this paper procedures for defining and verifying a statistical noise model are developed, and two multiplicative noise-smoothing algorithms are pre-sented. These two algorithms are computationally efficient and have the potential of achieving real-time or near-real-time processing. Several SEASAT SAR and SIR-B (Shuttle Imaging Radar) images are used for illustration.