This paper tests for long-run output convergence between a sample of eight Latin American countries and over the study period 1900-2003. The key contribution of this paper is in terms of the econometric methodology where non-stationarity of log real per capita income differentials is tested within a Markov regime-switching framework. In contrast to existing studies, this paper defines two new concepts of output convergence where one allows for the possibility that output differentials behaviour either switches between stationary and non-stationary regimes (partial convergence), or switches between stationary regimes characterised by differing degrees of persistence (varied convergence). Whereas standard univariate and panel data unit root testing clearly suggest that output differentials are non-stationary, employment of the regime-switching methodology indicates that most of the sample is characterised by the existence of two distinct stationary regimes. Furthermore, it is argued that the often-cited convergence rate of two per cent per annum is likely to be an underestimate.