In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff Index. During the last decade these parametres have been applied in Organic Chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules which have similar structural behaviours. Moreover, a wide range of generalized Kirchhoff Indexes for some networks have been introduced. The objective of the present work is to obtain the Kirchhoff Index for a wide range of composite networks known as cluster networks.