Investigations on the frequency behavior of AT-cut quartz crystals irradiated by X -, y-rays and fast neutrons have been carried out. Initial instability in frequency for ~Y~ and neutron irradiated crystals has been found. All the different radiations first give a negative frequency shift at lower doses which are followed, by positive frequency shift for increased doses. An explanation.of the results in terms of the fundamental crystal structure consideration is offered. Applications of the frequency results for radiation hardening are proposed.