  We prove a variant of the well-known Reidemeister-Schreier theorem for
finitely $L$-presented groups. More precisely, we prove that each finite index
subgroup of a finitely $L$-presented group is itself finitely $L$-presented.
Our proof is constructive and it yields a finite $L$-presentation for the
subgroup. We further study conditions on a finite index subgroup of an
invariantly finitely $L$-presented group to be invariantly $L$-presented
itself.
