[en] The application of the direct interaction approximation (DIA) to turbulent systems in which multi-time and -space scales exist is discussed. These different scales can be exploited to perform an asymptotic expansion of the dynamical governing equations prior to the application of the DIA. Based on a cursory examination of the Navier-Stokes equation, it is conjectured that such an approach may resolve some of the problems associated with the DIA. The problem of anomalous transport in tokamak fusion plasmas is another example of a problem which might benefit from such an approach. A new Hamiltonian method for deriving the nonlinear gyrokinetic equations which govern this system is discussed and shown to resolve many of the issues introduced by the recent application of Hamiltonian methods to this problem. This is followed by a reformulation of the DIA for systems in which there are two governing equations, instead of the usual one