  We introduce a quasi-equilibrium formalism in the theory of liquids in order
to obtain a set of coarse grained long time dynamical equations for the two
point density correlation functions. Our scheme allows to use typical
approximations devised for equilibrium to study long time glassy dynamics. We
study the Hypernetted Chain (HNC) approximation and a recent closure scheme by
Szamel. In both cases we get dynamical equations that have the structure of the
Mode-Coupling (MCT) equations in the long time region. The HNC approach, that
was so far used to get equilibrium quantities is thus generalized to a fully
consistent scheme where long-time dynamic quantities can also be computed. In
the context of this approximation we get an asymptotic description of both
equilibrium glassy dynamics at high temperature and of aging dynamics at low
temperature. The Szamel approximation on the other hand is shown to lead to the
exact Mode Coupling equation of G\"otze for equilibrium dynamics. We clarify
the way phase space is sampled according to MCT during dynamical relaxation.
