  If P, B, H are the algebras of the total space, the base space, and the
structure group of a locally trivial principal fibre bundle (QPFB), left
(right) gauge transformations are defined as automorphisms of the left (right)
B-module P which are adapted to the coaction of the Hopf algebra H and to the
covering related to the local trivializations. Covariant derivatives on a QPFB
are always transformed into covariant derivatives. This is true for connections
only for special choices of the differential structure on H and/or if one
restricts to algebra automorphisms. There are analogues of the classical
formulas relating local connection forms and their gauge transforms.
