  We consider generalized (possibly depending on fields as well as on
space-time variables) gauge transformations and gauge symmetries in the context
of general -- that is, possibly non variational nor covariant -- differential
equations. In this case the relevant principal bundle admits the first jet
bundle (of the phase manifold) as an associated bundle, at difference with
standard Yang-Mills theories. We also show how in this context the recently
introduced operation of $\mu$-prolongation of vector fields (which generalizes
the $\la$-prolongation of Muriel and Romero), and hence $\mu$-symmetries of
differential equations, arise naturally. This is turn suggests several
directions for further development. S0ome detailed examples are also given.
