A premixed flame propagating under flamelet conditions in turbulent flow is wrinkled by the fluid fluctuations at a multitude of scales. Traditional models of premixed combustion predict the flame speed based on global parameters from the reacting mixture. As a result, there is no information on intermediate to small scales, which are thought to play an increasingly important role in generating flame surface area as the flow becomes more turbulent. In an attempt to incorporate the entire spectrum of possible turbulent and flame length scales, a combustion model based on the eddy damped quasi-normal Markovian (EDQNM) theory has been developed. By applying the theory to the three-dimensional Navier-Stokes and modified Sivashinsky equations, one can derive transport equations for the scalar-velocity cross correlation spectrum as well as the scalar and velocity antocorrelation spectra. In this model, one can examine how flame surface area is affected by turbulent fluctuations over the entire spectrum. The model predicts that the turbulent flame speed is a function of the ratio of the turbulence intensity to the laminar flame velocity (γ) and the turbulence Reynolds number. The sensitivity of the flame speed to the Reynolds number particularly at high values of γ may explain some of the scatter in the data in the literature. The model also predicts a platean in the turbulent flame speed at large values of γ. This is connected to the behavior of the scalar autocorrelation spectrum, which approaches a passive scalar spectrum in the limit γ→∞, thereby yielding a bounded limit for the turbulent flame speed.