This paper analyzes a model for the competition dynamics of web sites in the Internet, based on the Lotka-Volterra competition equations. This model shows the well known appearance of a winner-take-all characteristic and is based in the nonvalidity of traditional offer and demand equilibrium theory of these kinds of markets. From the stability analysis of the model, we establish a series, of rules which are useful for defining strategies in the Internet market. One of the most important results that emerge from this simple model is the appearance of some unexpected phenomena related to the collaboration and competition between sites. (C) 2001 Elsevier Science B.V. All rights reserved.