Dynamic panel unit root tests are used to investigate the convergence hypothesis for a sample of developing countries. The data are real per capita GDP for the period 1960-95, covering 80 countries grouped into three broadly defined regions. The traditional cross-section unconditional convergence model produces no evidence of intra-regional convergence. However, panel unit root tests, interpreted as tests of the conditional convergence hypothesis, produce some evidence of intra-regional convergence for Africa and Latin America/Caribbean but only weak evidence for Asia/Pacific. Overall the results lend support to some of the main hypotheses of both neo-classical and new growth theory.