  Motivated by analogous results in locally conformal symplectic geometry, we
study different classes of G$_2$-structures defined by a locally conformal
closed 3-form. In particular, we give a complete characterization of invariant
exact locally conformal closed G$_2$-structures on simply connected Lie groups,
and we present examples of compact manifolds with different types of locally
conformal closed G$_2$-structures.
