Let G be a simple and simply connected algebraic group over a field. We can attach to a it the sheaf of conformal blocks: a vector bundle on M_g whose fibres are identified with global sections of a certain line bundle on the stack of G-torsors. We generalize the construction of conformal blocks to the case in which G is replaced by a "twisted group" defined over curves in terms of covering data. In this case the associated conformal blocks define a sheaf on a Hurwitz stack and have properties analogous to the classical case.