The irreversibility lines (ILs) for high quality REBa2Cu3O7-? crystals (RE = Y and Nd) were determined from complex magnetic susceptibility measurements. The effect of twins on the crystals was also investigated by comparing the ILs for the YBa2Cu3O7−? samples with and without twins. The YBa2Cu3O7−? single crystals were grown through the flux method while the intergrowth Nd1/2Y1/2Cu3O7-? crystals were grown using the melt-textured growth technique. Stoichiometric analysis through XRD and EMPA showed a single phase YBa2Cu3O7−? crystal and a dual phase (Nd/Y)Ba2Cu3O7−? composite crystal. The ILs showed the same power law relation, Hdc µ (1 − t)n for all samples investigated. The ILs were also found to be dependent on ac field amplitude and frequency. The ILs became steeper and shifted to higher temperatures for increasing ac field frequency. Opposite trends were observed for increasing ac field amplitude. The empirical formula Hdc = k[(1-t)/ln(f0/f)]n was obtained that accounted for the simultaneous ac field amplitude and frequency dependence. The characteristic frequency f0 was interpreted to be some limiting parameter, a finding supported by the nonlinear flux diffusion model. The exponent n was found to be dependent on both ac field and frequency. It was found that detwinning increased the Tp−Hdc dependence. In addition, there was a weak frequency dependence of the ILs for the intergrowth (Nd/Y)Ba2Cu3O7−? in contrast to a highly responsive “clean” YBa2Cu3O7−? single crystals. This difference strongly indicates an intrinsic characteristic of high TC superconductors.