A new approach to construction of turbulence models that allows modeling of fluctuating components in the form of an infinite number of random quantities has been suggested. The first part of the work deals with the technique of construction of the k-epsilon-type model. The calculations show a great expansion of the possibilities of models. Among the problems under solution there are calculations of spectrum, coherent structures, modeling of the bypass transition, etc. The theory that forms the basis of the approach is confirmed experimentally. (C) 2009 Elsevier Ltd. All rights reserved.