In an infinite network X, the extremal elements for a base of the cone of positive superharmonic functions in X are determined and an integral representation for this cone of functions is given by using the Choquet integral representation theorem. Later, a similar representation is given to the class of non-negative separately superharmonic functions in a product network X x Y, but without proving the uniqueness of the representing measures. However if we restrict to a subclass of non-negative separately superharmonic functions, called here the balanced functions, then the representing measure is unique. © 2016, Editura Academiei Romane. All rights reserved.