  In this paper we focus on the relations between the derived categories of a
Koszul algebra and its Yoneda algebra, in particular we want to consider the
cases where these categories are triangularly equivalent. We prove that the
simply connected Koszul algebras are derived equivalent to their Yoneda
algebras. We consider derived discrete Koszul algebras, and we give necessary
and sufficient conditions for these Koszul algebras to be derived equivalent to
their Yoneda algebras. Finally, we look at the Koszul algebras such that they
are derived equivalent to a hereditary algebra. In the case that the hereditary
algebra is tame, we characterize when these algebras are derived equivalent to
their Yoneda algebras.
