This paper is devoted to analyze the special class of turbulent premixed flames that we call intermediate steady propagation (ISP) flames. These flames an common to industrial premixed combustion chambers which operate at intensive turbulence when velocity pulsations are significantly higher than the flamelet combustion velocity. They are characterized by a practically constant turbulent combustion velocity, controlled by turbulence, chemistry and molecular processes, and by an increasing flame width, controlled mainly by turbulent diffusion. The main content of this work is a description of physical backgrounds and outcome of the original asymptotic (i.e., valid at high Re and Da numbers) premixed combustion model, that, from a methodological point of view, is close to Kolmogorov analysis of developed turbulence at high Re numbers. Our analysis starts from the thickened and strongly wrinkled flamelet combustion mechanism. Quantitative results for this model are based on the Kolmogorov assumption of the equilibrium fine-scale turbulence and on additional assumption of the universal small-scale structure of the wrinkled flamelet sheet. From this background, it is possible to deduce formulas for the thickened flamelet parameters and the flamelet sheet area and hence the turbulent combustion velocity of the premixed flame. These formulas are used for the closure of the combustion equation written in terms of a progress variable leading to the so-called turbulent flame closure (TFC) model for the numerical simulation of ISP flames. Consistent with the ISP flames, in this work the concept of counter-gradient transport phenomenon in premixed combustion is analyzed. (C) 2000 Elsevier Science Inc. All rights reserved.