  The classical Liouville Theorem on conformal transformations determines local
conformal transformations on the Euclidean space of dimension $\geq 3$. Its
natural adaptation to the general framework of Riemannian structures is the
2-rigidity of conformal transformations, that is such a transformation is fully
determined by its 2-jet at any point. We prove here a similar rigidity for
generalized conformal structures defined by giving a one parameter family of
metrics (instead of scalar multiples of a given one) on each tangent space.
