Two categories of evolutionary models are analyzed. The first category is the so-called autogenesis phenomenon. The emergence of self-organization, which has been discussed previously by Csanyi and Kampis is verified. The model is extended to an interrelated multi-level autogenesis system. Similarly, self-organization is observed in a hierarchical order for ea.ch level. The second category is the optimization model ol evolution. An ongoing process of consecutive LP runs associated with random perturbation of the parameters at each step, is designed to simulate the evolutionary mechanisms (mutations, variations and selection) and the population dynamics of a hypothetical ecological system. Two diihu'ent LP ajrproaches for Lotka-Volterra systems are compared and contrastc'd. A brief history of evolution a.nd some mathematical models that have been constructed up to date are also descrilred in the beginning chapter.