An analysis of the transient motion of ledged interphase boundaries is presented where volume diffusion of solute in the matrix to the riser of the step is assumed to control the growth rate. The analysis leads to a nonlinear integral equation governing step motion and can be applied in principle to situations involving many interacting steps. Detailed attention is given to the case of a single step in an infinite medium where comparisons are made with numerical results of Enomoto (obtained by finite difference solution of the diffusion equation). Attention is also given to transient motion in a medium of finite extent. The treatment here thus generalizes the steady-state theory of Atkinson.