[en] The combined angular and lateral spread of an initially narrow well-collimated ion beam by multiple scattering in a random medium is evaluated theoretically in the small-angle approximation, and measured experimentally for a 50 keV argon beam incident on a xenon gas target. By means of an approximation for the transport cross section averaged over target thickness - the validity of which is tested theoretically - the double-differential distribution in angular and lateral spread can be factorized in such a way that only (known) angular distributions occur in the final expression. Experimental tests have been performed for the special case where angular and lateral spread lie in one plane with the beam. The agreement with the theoretical profiles is very good with regard to the scaling with target thickness, the orientation in the α - β - plane (α=angular, β= lateral spread), and the absolute dimensions. Discrepancies occur in the tails at large values of α and β. These differences are expected to be much less pronounced at larger values of the scaled target thickness tau, i.e. for tau > approximately 0.1. (Auth.)