A fundamental understanding of nanoscaled materials has become an important challenge for any technical applications. For magnetic nanoparticles, the investigations are in particular stimulated by the magnetic storage devices. In this chapter we present, in the frame of the discrete dipole approximation, a theory of the magnon propagation in quasi-one-dimensional resonant structures, composed of nanometric magnetic cluster chains and adsorbed clusters near the chains. Results for the transmission and reflection properties, the phase of the transmission amplitude, the state phase shift, and the variation of the density of states of such nanometric networks are discussed, as a function of the frequency of the excitations and the physical or geometrical properties of the circuits, within the framework of the Green’s function method. The production of these circuits utilizes the most advanced surface technologies and represents one of the most important challenges for the next decade. All such circuits exhibit a variety of interference effects in their transport properties. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches.