  A method is proposed for generalizing the Euclidean Taub-NUT space, regarded
as the appropriate background of the Dirac magnetic monopole, to non-Abelian
Kaluza-Klein theories involving potentials of generalized monopoles. Usual
geometrical methods combined with a recent theory of the induced
representations governing the Taub-NUT isometries lead to a general conjecture
where the potentials of the generalized monopoles of any dimensions can be
defined in the base manifolds of suitable principal fiber bundles. Moreover, in
this way one finds that apart from the monopole models which are of a
space-like type, there exists a new type of time-like models that can not be
interpreted as monopoles. The space-like models are studied pointing out that
the monopole fields strength are particular solutions the Yang-Mills equations
with central symmetry producing the standard flux of $4\pi$ through the
two-dimensional spheres surrounding the monopole. Examples are given of
manifolds with Einstein metrics carrying SU(2) monopoles.
