Let X be a Hilbert C∗-module over a C∗-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C∗-module X called operator algebras with property K and operator algebras with property Z, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.
