A limitation on the growth rate is proposed in the multinucleation regime. Spherulite growth rates of poly(p-phenylene sulfide) (PPS) in thin films of 1 mu m down to 0.2 mu m are measured in the range of crystallization temperature from 190 degrees C to 275 degrees C. Dependence of the growth rate on film thickness is also measured at the crystallization temperature. Growth rates vary by 4 orders of magnitude and are independent of film thickness. Since the film thickness is nearly equal to the width of the growth surface under the conditions in this work, the growth rate is independent of the width of growth surface. This means that PPS spherulites grow in a multinucleation regime. On the basis of the Limitation on growth rate we proposed in this paper, the range of growth rate has to be less than 10(2) under the conditions investigated. Failure of the present nucleation theory is concluded from the results. To explain these results, thermal insensitivity of step velocity must be discarded.