We present a general Cournot model in which each ¯rm may sell multiplequality-di®erentiated products. We use an upgrades approach, working not with theactual 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 notnecessarily to the supply of complete products. A ¯rm's product line is determinedby the properties of demand, its costs, and competitor characteristics. For symmet-ric ¯rms, these determinants reduce to returns to quality and changes in demandelasticity as quality increases. For asymmetric ¯rms whose (potentially endogenous)technological capabilities are de¯ned by their maximum feasible qualities, gaps inproduct lines are determined precisely by the capabilities of lesser rivals. Strategiccommitment to product lines prior to quantity competition is considered. Incentivesto so commit are markedly di®erent from those under price-setting models....