Nuclear magnetic resonance far off the Larmor frequency - nonsecular resonances in CaF$_2$

High field magnetic resonance of nuclear spins is normally carried out at or near the Larmor frequency Ω0. Here, we report an observation of nonsecular nuclear spin resonances far off Ω0. These originate from nonsecular terms of the nuclear spin-spin interaction and provide means for the control of coupled two level systems. In systems of equivalent nuclear spins, nonsecular resonances were predicted to lead to anomalous, fast relaxation of the nuclear spin polarization. We report experimental results that are in excellent agreement with the predicted behavior.