A theorem is presented describing a transformation by means of which it is possible to assign to an elementary multiport with fairly general constitutive equations (including all kinds of controlled sources, nullors, ideal transformers, etc.) a modified multiport with the same all-pole terminal behavior. The branch set of this modified multiport is augmented with so called auxiliary branches whereas its constitutive equations are always in conductance form. Therefore an interconnection of a family of multiports transformed in this manner can always be analyzed by means of a system of nodal voltage equations. It will be shown that this system of equations is equivalent to a system of modified nodal voltage equations set up for the network that is an interconnection of the elementary multiports originally given.