Let A be a C^*-algebra and \alpha a *-endomorphism of A. The analogue of Pimsner-Voiculescu exact sequences are obtained for the pair (A, \alpha). We prove that the corresponding Toeplitz algebra remains KK-equivalent to A. We also consider the situation where a semigroup (\alpha^t)_{t\in R_+} of *-endomorphisms is acting on A and formulate similar exact sequences. In this part we use the language of Connes-Higson E-theory.