We consider a system consisting of a Λ-type atom and a V-type atom which are individually trapped in two spatially separated cavities that are connected by an optical fiber.The evolutions of the excitions of atom 1,atom 2,cavity A,cavity B and fiber mode are given.We discuss the influence of cavity-fiber coupling coefficient on the excitions.The results obtained by the numerical method show that the excitions of cavity A and cavity B decrease with increase of the cavity-fiber coupling coefficient.On the other hand,the excition of fiber mode shows a nonlinear variation with increase of the cavity-fiber coupling coefficient.