  We consider the recursion operators with nonlocal terms of special form for
evolution systems in (1+1) dimensions, and extend them to well-defined
operators on the space of nonlocal symmetries associated with the so-called
universal Abelian coverings over these systems. The extended recursion
operators are shown to leave this space invariant. These results apply, in
particular, to the recursion operators of the majority of known today
(1+1)-dimensional integrable evolution systems. We also present some related
results and describe the extension of them and of the above results to
(1+1)-dimensional systems of PDEs transformable into the evolutionary form.
Some examples and applications are given.
