One of the most influential evolutionary model in Nelson and Winter's book is the one dealing with industrial dynamics (chapter 12). From that model came out meaningful insights about market structure and technological change relationship. Despite the improvements made by evolutionary models that arose in this field since Nelson and Winter's book, this stream of models still shares some of the original limitations of Nelson and Winter's model, all them related to technological search. Thus, this article aims to make a technological search model that has properties (technological cumulativeness, asymmetrical R&D spillovers and knowledge accumulation and depreciation) which manage to overcome those analytical limitations.