  In this paper, colorless bilocal fields are employed to study the large $N$
limit of both fermionic and bosonic vector models. The Jacobian associated with
the change of variables from the original fields to the bilocals is computed
exactly, thereby providing an exact effective action. This effective action is
shown to reproduce the familiar perturbative expansion for the two and four
point functions. In particular, in the case of fermionic vector models, the
effective action correctly accounts for the Fermi statistics. The theory is
also studied non-perturbatively. The stationary points of the effective action
are shown to provide the usual large $N$ gap equations. The homogeneous
equation associated with the quadratic (in the bilocals) action is simply the
two particle Bethe Salpeter equation. Finally, the leading correction in
$1\over N$ is shown to be in agreement with the exact $S$ matrix of the model.
