The nature of competitive equilibrium is investigated for brands competing in a multi-attribute product space when consumer preferences for product attributes follow nonuniform distributions. Subgame-perfect equilibria are established in a 2-stage game, where firms choose positions in the first stage and prices in the 2nd stage. Two types of entry scenarios are investigated. In the first, the number of brands is given exogenously, and all of them choose positions simultaneously. In the 2nd scenario, firms enter in sequence, and the early entrants can choose strategies to deter the entry of later entrants. The equilibria for 2, 3, and 4 brands for consumer preferences that follow a beta distribution are found. Nonuniform distributions result in equilibrium configurations that are substantially different from those obtained for uniform consumer distributions. In addition, entry deterring positioning strategies are characterized and the ways in which they vary with the distribution of consumer preferences are examined.