  The Fredholm index of unbounded operators defined on generalized solutions of
nonlocal elliptic problems in plane bounded domains is investigated. It is
known that nonlocal terms with smooth coefficients having zero of a certain
order at the conjugation points do not affect the index of the unbounded
operator. In this paper, we construct examples showing that the index may
change under nonlocal perturbations with coefficients not vanishing at the
points of conjugation of boundary-value conditions.
