  The Gell-Mann and Low switching allows to transform eigenstates of an
unperturbed Hamiltonian $H_0$ into eigenstates of the modified Hamiltonian $H_0
+ V$. This switching can be performed when the initial eigenstate is not
degenerate, under some gap conditions with the remainder of the spectrum. We
show here how to extend this approach to the case when the ground state of the
unperturbed Hamiltonian is degenerate. More precisely, we prove that the
switching procedure can still be performed when the initial states are
eigenstates of the finite rank self-adjoint operator $\cP_0 V \cP_0$, where
$\cP_0$ is the projection onto a degenerate eigenspace of $H_0$.
