  We consider two examples of dynamical semigroups obtained by singular
perturbations of a standard generator which are special case of unbounded
completely positive perturbations studied in detail in [10]. In the section 2
we propose a generalization of an example from [1] aimed to give a positive
answer to a conjecture of Arveson. In the section 3 we consider in greater
detail an improved and simplified construction of a nonstandard dynamical
semigroup outlined in our short communication [13].
