On the basis of the analysis of scientific ideas reflecting the law in the structure and functioning the biological structures of a brain, and analysis and synthesis of knowledge, developed by various directions in Computer Science, also there were developed the bases of the theory of a new class neural-like growing networks, not having the analogue in world practice. In a base of neural-like growing networks the synthesis of knowledge developed by classical theories - semantic and neural of networks is. The first of them enable to form sense, as objects and connections between them in accordance with construction of the network. With thus each sense gets a separate a component of a network as top, connected to other tops. In common it quite corresponds to structure reflected in a brain, where each obvious concept is presented by certain structure and has designating symbol. Secondly, this network gets increased semantic clearness at the expense owing to formation not only connections between neural by elements, but also themselves of elements as such, i.e. here has a place not simply construction of a network by accommodation sense structures in environment neural of elements, and purely creation of most this environment, as of an equivalent of environment of memory. Thus neural-like growing networks are represented by the convenient apparatus for modeling of mechanisms of teleological thinking, as a fulfillment of certain psychophysiological of functions.