  In this article we give the realization of the Klein's Program for
geometrical structures (Riemannian spaces and fiber bundles with connection)
with arbitrary variable curvature within the framework of infinite deformed
groups. These groups generalize gauge groups to the case of nontrivial action
on the base space of bundles with use of idea of groups deformations.
  We also show that infinite deformed groups give a group-theoretic description
of gauge fields (gravitational field with its metric or vierbein part similarly
to gauge fields of internal symmetry) which is alternative for their
geometrical interpretation.
