  We study the renormalization problem for the Hartree--Fock approximation of
the $O(N)-$invariant $\phi^4$ model in the symmetric phase and show how to
systematically improve the corresponding diagrammatic resummation to achieve
the correct renormalization properties of the effective field equations,
including Renormalization--Group invariance with the one--loop beta function.
These new Hartree--Fock dynamics is still of mean field type but includes
memory effects which are generically nonlocal also in space.
