AbstractIt is required to interconnectnexisting networks in the plane by new links of minimal total length. We assume that the edges of the networks are straight and that it is possible to make connections along the edges or to the vertices. The use o f Steiner points is also allowed. Though the theoretical number of solutions to the problem is uncountable, we prove that it is enough to consider a finite set of locally optimal solutions with a limit on the number of connections along edges. This makes it possible to solve the problem in finite time by methods similar to those used for the Euclidean Steiner tree problem. The problem can be generalized to include flow‐dependent costs for the various link