  The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of
Slater determinants to approximate the electronic $N$-body wave function of a
relativistic molecular system, resulting in a coupled system of nonlinear
eigenvalue equations, the MCDF equations. In this paper, we prove the existence
of solutions of these equations in the weakly relativistic regime. First, using
a new variational principle as well as results of Lewin on the
multiconfiguration nonrelativistic model, and Esteban and S\'er\'e on the
single-configuration relativistic model, we prove the existence of critical
points for the associated energy functional, under the constraint that the
occupation numbers are not too small. Then, this constraint can be removed in
the weakly relativistic regime, and we obtain non-constrained critical points,
i.e. solutions of the multiconfiguration Dirac-Fock equations.
