The magnetic-field dependence of the irreversibility temperatures follows an H = a[1-T(r)(H)/T(c)(0)]n relationship with n approximately-equal-to 1.5, for pure and alloyed YBa2(Cu(1-x)M(x))3O7+delta with x = 0 and 0.02, where M = Al, Fe, Ni, and Zn, measured for an applied field parallel to the c axis. However, for M = Ni and x = 0.04 and 0.06, n approximately-equal-to 2.0. This relationship is not applicable for either Bi2Sr2CaCu2O8 or (Bi,Pb)2Sr2Ca2Cu3O10 powders. It is also shown that the irreversibility temperature is a strong function of the magnetic hysteresis width DELTA-M for pure and alloyed YBa2Cu3O7. These results and the measurements of the flux creep DELTA-M(t) for these specimens suggest that T(r)(H) is a depinning line rather than a lattice melting or glass-to-liquid phase-transition temperature. However, the conventional flux-creep model cannot account for all of the observed temporal dependences of DELTA-M(t).