Anomalous two-stage spherulite growth has been observed in poly(aryl ether ketones) during isothermal crystallization. The first stage consists of a conventional growth with Maltese-cross pattern at a lower growth rate. The morphology shows a smooth interface, dense structure and negative birefringence. The second stage grows in the form of "aggregate" at a higher rate. The morphology shows an open dendrite structure without preferred optical orientation. The second morphology is also termed the "overgrowth." The occurrence of overgrowth is favored only near the maximum growth rate region and diminishes in the slow growth region. The transition of the two-stage growth is attributed to the change of growth direction of the constituent lamellae. We have confirmed this by microbeam small-angle light-scattering measurements. The lamellar structures in both growth stages were followed by time-resolved small-angle synchrotron x-ray scattering. It was found that the lamellar structures of the crystals formed at both stages are the same. A possible explanation for the two-stage growth is the interface breakdown caused by large perturbations of local composition and/or stress fields.