The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and negative returns.In this paper we propose a process that allows the simultaneous modelling of skewed conditional returns and different dynamics in their conditional second moments. The main stochastic properties of the model are analyzed and necessary and sufficient conditions for weak and strict stationarity are derived.An application to the daily returns on the principal index of the London Stock Exchange supports our model when compared to other frequently used GARCH-type models, which are nested into ours.