We propose new dynamical equations to describe fully developed turbulence. We begin with the Wyld equations (WE), which are exact solutions of the NSE. The WE, and their Langevin‐like representation, show that nonlinearities induce a turbulent forceft(k) and a turbulent viscosity &ngr;t(k), which are given by an infinite series of Wyld diagrams. The series for &ngr;t(k) is renormalizable, and its sum can be found using RNG methods. The result, Eq. (2a), holds for stirring forcesfextwith an arbitrary correlation function &fgr; and generalizes previous RNG results, which neglectedftand were limited to power law &fgr;∼k1−2&egr;. To recover Kolmogorov law, these earlier RNG‐based theories were forced to introduce anadhocstirring force with a prescribed &fgr;∼k−3. By contrast, we show that ∼k−3belongs to &fgr;˜, which is the correlation function offt, and that in the inertial rangeft≫fext. The series for &fgr;˜ cannot be summed because of a nonrenormalizable infrared divergence (IR) with an infinite number of divergent irreducible diagrams. To overcome this difficulty, we use the well‐accepted notion of local energy transfer and we derive an expression for the energy flux &Pgr;(k), Eq. (2d), as well as a dynamical equation for the energy spectrumE(k), Eq. (2b). We also construct the dynamical equations for Reynolds stress spectra (solved in papers II and III). An analogous approach is developed for the temperature field. The model contains no free parameters. Some of its predictions are Kolmogorov spectrumE(k)∼k−5/3with Ko=5/3, in agreement with recent data; temperature spectrum in the inertial‐convective regionE&thgr;∼Ba &egr;¯−1/3&egr;&thgr;k−5/3, in agreement with the data; Batchelor constant Ba=&sgr;t Ko. In addition, in papers II and III we carry out extensive comparisons with the laboratory, DNS, LES data, and phenomenological models. The model can be used to construct a subgrid model for LES calculations. ©1996 American Institute of Physics.