The results of previous time-series studies of the income convergence hypothesis indicate that practically no African economies are systematically closing their income gap with the rich world. This implies that almost the entire continent is not 'developing' in the literal sense of the term. We argue that this finding reflects the assumptions of the discrete-break unit-root tests previously employed and the sample period chosen. We re-assess the hypothesis for 43 African economies using Fourier-type unit-root tests and find that as many as 18 are currently catching-up with the US. However, most only began to do so after the mid-1990s. (C) 2014 Elsevier Ltd. All rights reserved.