We have studied the energy spectrum of a system formed by two concentric, coupled, semiconductor quantum rings. We have investigated the effect of a uniform magnetic field applied along the rings axis, on the energy spectrum of the system. We found that the spectrum of the coupled rings with similar confinement length corresponds roughly to the superposition of the spectra of two separate rings, although modified by the anticrossings produced among different states of the individual rings with same angular momentum. The Aharonov-Bohm oscillations do not have a definite period.
