Abstract： In this paper, an automous n-species competitive Lotka-Volterra systems are studied. For each r ≤ n , we show that if the coefficients satisfy certain inequalities, then any solution with strictly positive initial values has the property that n - r of its components vanish, whilst the remaining r components asymptotically approach a canonical solution of an r-dimensional restricted system. In other words, r of the species being modeled survive whilst the remaining n - r are driven to extinction. Our results bridge the gap among all known relational results.