An approximate analytic solution to the infinite-medium slowing down equation is obtained for a weakly absorbing mixture of isotopes. It derives from a moment expansion of the integral equation and, by truncation, involves the average lethargy gain and the average square of the lethargy gain per collision in the mixture. It applies to the vicinity of a resonance if the isotope masses are not much different from each other or if the scattering power (ξ ΣS) of the resonant isotope at the resonance peak is much higher than the scattering power of the background. It offers a simple description of the strong fluctuations in the collision density caused by wide or strong resonances of light and structural elements in fast mixtures. An important application of the theory is the evaluation of group cross sections. The theoretical estimate of the group removal cross section was compared with numerically-exact values and a discrepancy of a few percent was found.