We have studied a mesoscopic double-ring system connected in parallel and coupled to two electron reservoirs. The system is composed of one-dimensional ordered chains, and the two rings are threaded by magnetic fluxes Phi(1) and Phi(2), respectively. In the framework of the tight-binding model, the analytical and numerical calculations show that the transmission coefficient T is periodic in fluxes Phi(1), and Phi(2) with a period 2 Phi(0),Phi(0)=hc/e. For the system there are resonant states (T=1) and antiresonant states (T=0), the distribution of which displays a very remarkable symmetry. [References: 19]
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