A theoretical study is made of geometry average statistical speckles of the intensity of a broadband dispersed laser beam which is spatially coherent in the initial plane z = 0. Two-dimensional distributions of random intensity are numerically simulated, which make it possible to trace transformation of speckle patterns in the course of the beam propagation. The correlation functions and power spectra of random intensity are calculated to show how the characteristic dimensions and the shape of speckles vary depending on longitudinal coordinate z, the width and shape of the frequency spectrum and also the degree of dispersion of the light beam. Analytical expressions are derived which show that the speckle dimensions increase in the longitudinal direction as well as in the direction of the dispersion as the distance from the initial plane increases. Limit value (at z → ∞ ) of the speckle width in the direction of the beam dispersion is calculated.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.