By using the theory of the strongly continuous cosine family, the principle of contraction mapping and the Gronwall-Bellman type integral inequality,the existence and relevant properties of solutions of a second order semi-linear and nonhomogeneous operator-differential system in a Banach space are investigated. It is proved that the system has a unique solution and it continuously depends on the initial values under certain conditions; furthermore, the boundedness and the prior estimation on the solution are also presented.

operator-differential system； solution； existence； uniqueness； Lipschitz condition