  We suggest the method for group classification of evolution equations
admitting nonlocal symmetries which are associated with a given evolution
equation possessing nontrivial Lie symmetry. We apply this method to
second-order evolution equations in one spatial variable invariant under Lie
algebras of the dimension up to three. As a result, we construct the broad
families of new nonlinear evolution equations possessing nonlocal symmetries
which in principle cannot be obtained within the classical Lie approach.
