It is important to predict extreme electricity demand in power utilities as the uncertainties in the future of electricity demand distribution have to be taken into consideration to achieve the desired goals. The study focused on the prediction of extremely high conditional quantiles (between 0.95 and 0.9999) and extremely low quantiles (between 0.001 and 0.05) of electricity demand using South African data. The paper discusses a comparative analysis of the additive quantile regression model with an extremal mixture model and a nonlinear quantile regression model. The estimated quantiles at each level were then combined using the median approach. The comparisons were carried out using daily peak electricity demand data ranging from January 1997 to May 2014. Proper scoring rules were used to compare the three models, and the model with the smallest score was preferred. The results could be useful to system operators including decision-makers in power utility companies by giving insights and guidance for future electricity demand patterns. The prediction of extremely high quantiles of daily peak electricity demand could help system operators know the possible largest demand that will enable them to supply adequate electricity to consumers and shift demand to off-peak periods. The prediction of extreme conditional quantiles of daily peak electricity demand in the context of South Africa using additive quantile regression, nonlinear quantile regression, and extremal mixture models has not been performed previously to the best of our knowledge.