This paper examines whether accounting for structural changes in the conditional variance process, through the use of Markov-switching models, improves estimates and forecasts of stock return volatility over those of the more conventional single-state (G)ARCH models, within and across selected African markets for the period 2002-2012. In the univariate portion of the paper, the performances of various Markov-switching models are tested against a single-state benchmark model through the use of in-sample goodness-of-fit and predictive ability measures. In the multivariate context, the single-state and Markov-switching models are comparatively assessed according to their usefulness in constructing optimal stock portfolios. Accounting for structural breaks in the conditional variance process, conventional GARCH effects remain important in capturing heteroscedasticity. However, those univariate models including a GARCH term perform comparatively poorly when used for forecasting purposes. In the multivariate study, the use of Markov-switching variance-covariance estimates improves risk-adjusted portfolio returns relative to portfolios constructed using the more conventional single-state models. While there is evidence that some Markov-switching models can provide better forecasts and higher risk-adjusted returns than those models which include GARCH effects, the inability of the simpler Markov-switching models to fully capture heteroscedasticity in the data remains problematic.