In this paper, we focus on the nature of demand and competitive response in the market for private label and national "branded'' grocery products. Specifically, we employ less restrictive functional forms than used in prior research. Specifically, we incorporate LA/AIDS demands and the corresponding price reaction equations to estimate consumer price sensitivities and supply side price strategies for national brand and private label products. Oligopolistic price interdependence is explored further by specifying brand share, brand Herfindahl, and a measure of the structure of the local retail markets in the supply side relations to evaluate explicitly the impact of market structure. In our empirical analysis, we estimate a system of market share and price equations simultaneously in order to examine (i) the determinants of the demand response to pricing and promotion decisions and (ii) the determinants of private label and national brand pricing behavior. Using data for 143 food product categories and 59 geographic markets, we develop a model that captures the variation in private label-national brand share and pricing across categories and markets. Key findings include: (i) demand response to price and promotion is decidedly asymmetric, (ii) price followship between private labels and national brands is positive, but not strong, and (iii) markets characterized by higher national brand market share and higher supermarket concentration tend to have higher prices for both national brands and private labels.