The diffusion of products that compete in the marketplace is a strategic issue for market analysts. In this paper, we introduce two models that are essentially extensions of the class of the Lotka-Volterra competition models that have a consolidated history in the literature. The need to recover an excellent competition framework that was applied in innumerable disciplines, from biology to physics and so on, has essentially motivated this extension. The principal and appealing feature in these models is that they offer a definition of residual market that is more general with respect to the existing competition models available in literature, allowing that competing products contribute with different weights to perceived residual markets.