In this paper some general phenomena are described for not necessarily systemeric so–called generalized Schrödinger semigroups (or generalized absorption/exciatation semigroups). These results are also applicable in case we consider Schrödinger semigroups onRv. In particular we describe some results on integral kernels: continuity, pointwise inequalities, ultracontractivity etc.For these inequalities we use a kind of stochastic bridge measure. The operatorHis a closed linear extension of the operatorH0+Vin the spaceC0(E) HereEis a locally compact second countable Hausdorff space and –H0is supposed to generate a Feller semigroup inC0(E). Results inLp(E,m) are also availale. Some examples are given