In this paper a combined dissociative and kick-out model for impurity diffusion in semiconductors is studied. The mechanism has been used, for example, as a model for the diffusion of chromium in gallium arsenide. The authors derive asymptotic solutions for both one- and two-dimensional surface source (indiffusion) problems and for a one-dimensional outdiffusion problem and illustrate their results by plotting impurity profiles and (for the two-dimensional problem) contours of constant concentration. By varying the appropriate parameter in the one dimensional asymptotic solutions, it is possible to describe the transition from profiles characteristic of the kick-out mechanism to those of the dissociative mechanism. Aspects of the transition from dissociative to kick-out behaviour are also obtained for the two-dimensional problem.