A general and systematic formulation based on the finite-element method, modified nodal analysis and multi-field system approach is presented for the analysis of multiple magnetic field systems that are electrically interconnected through circuit networks in the frequency domain. This approach permits simultaneous solution of any number of 2-D Cartesian and axisymmetric problems by considering the electrical terminals of each finite-element model as nonnatural elements of the modified nodal analysis, allowing their systematic incorporation into the global system of equations. This way, arbitrary electrical network topologies can be readily analyzed, where the magnetic systems are no more than simple elements of the circuit system. Moreover, a unified building block is introduced for the 2-D and axisymmetric models, leading to easy computer implementation. The effectiveness of our formulation is tested by determining the electromagnetic behavior of a double-squirrel cage induction motor that is connected to three feeding transformers. A 2-D Cartesian finite-element model is employed for the three-phase motor, whereas an axisymmetric representation is used for each transformer. Hence, four finite-element models are simultaneously solved, which are electrically coupled through circuit elements. Lumped circuit parameters model the end effects of the motor squirrel cage and stator as well as the associated stator feeding circuits. Previous work only considers coupling of Cartesian systems, while our formulation expands the capabilities of quasi-3-D finite-element modeling by systematically coupling 2-D and axisymmetric finite-element models.