We present a general Cournot model in which each flrm may sell multiple quality-difierentiated products. We use an upgrades approach, working not with the actual products, but instead with upgrades from one quality to the next. The prop- erties of single-product Cournot models carry over to the supply of upgrades, but not necessarily to the supply of complete products. A flrm's product line is determined by the properties of demand, its costs, and competitor characteristics. For symmet- ric flrms, these determinants reduce to returns to quality and changes in demand elasticity as quality increases. For asymmetric flrms whose (potentially endogenous) technological capabilities are deflned by their maximum feasible qualities, gaps in product lines are determined precisely by the capabilities of lesser rivals. Strategic commitment to product lines prior to quantity competition is considered. Incentives to so commit are markedly difierent from those under price-setting models.