for the treatment of transport has been to neglect time correlations altogether, i.e. to consider a velocity field $\u$ such that $\langle u_\alpha (\x,t)u_\beta (0,0)\rangle = 
U_{\alpha\beta}(\x)\delta(t)$: the so called Kraichnan model [@kraichnan94]. In this model, Eulerian and Lagrangian time statistics trivially coincide in what is the zero order of some perturbation theory in powers of the correlation time of the turbulence. It has been possible, in particular, to determine the anomalous scaling exponents of a passive scalar injected at large scales in the velocity field [@chertkov95; @gawedzki95; @frisch98; @gat98]. The origin of this success is that, although the time structure of the velocity correlation is lost, that of the relative displacement, whose geometrical properties determine the passive scalar correlations, is preserved [@gat98a; @pumir00; @celani01]. (For instance, particle pair separation still obeys Richardson diffusion).

The question, at this point, is how to introduce finite correlation times in a perturbative manner, but preserving the Lagrangian nature of correlations. There are practical reasons to do this. One motivation, of course, is to be able to determine the time correlations of the particle velocities. Lagrangian dispersion models [@thomson87; @thomson90; @borgas94] are based on the adoption of prescriptions on the form of these time 