Nonlinear growth of polymer spherulites has been repeatedly reported in blends containing a low-molecular weight amorphous polymer. A new explanation for this behaviour is proposed. Results of numerical simulations of the growth of lamellar stacks are presented. The model incorporates diffusion of amorphous polymer and assumes that the lamellar growth rate is depressed by the presence of amorphous chains at the growth front. It is shown that steady-state growth is reached only after long times when the diffusion coefficient of amorphous chains is large or when the lamellar growth rate is small. It is proposed that nonlinear growth in blends containing a low-molecular weight amorphous polymer (large diffusion coefficient) is, in some cases, due to the long times needed for a steady state to be reached and not a diffusion-limiting process.