The hysteretic magnetic properties of ring-shaped single crystals of YBa2Cu307_ ~ and Bi2Sr2CaCu20 s have been investigated using a VSM for long time-scale measurements and an electronic integration magnetometer for a.c. hysteresis measurements at frequencies from 10 Hz to 1 kHz. Measurements of the bulk critical current and its temperature, field and materials processing dependence can be made without the need for attaching leads or having to subdivide the crystal to investigate the scaling dependence of the magnetization on sample size. A strong frequency dependence of the magnetic hysteresis is observed, which is related to the non-linear V(I) characteristics of the ring. Such characteristics result in flux creep at low frequencies and strongly frequency dependent magnetic hysteresis at high frequencies and sweep amplitudes. Flux penetration into the single crystal ring samples is determined by an effective time constant involving the ring inductance and the non-linear V(I) characteristics. Computer models are used to determine the time dependence of flux penetration into a superconducting slab following a linear field ramp and into a superconducting ring in an a.c. field using illustrative E(J) characteristics. Computed results reproduce the qualitative features of our experimentally derived a.c. magnetization measurements.