The analytical magnetization versus time expressions for several flux‐pinning models for high‐Tcsuperconductors are deduced. Magnetic relaxation and hysteresis studies have been performed on a zone‐melted YBa2Cu3O6+xsample by SQUID. Nonlogarithmic magnetization decay is observed at relatively high temperatures; we attribute this to the nonlinearU(J) relationship which may arise from the local pinning potentialUp(x), rather than collective pinning. At 70 K, the experimental data fits extremely well to the expressionM(t)=M0+a(T)ln ln(t/&tgr;) which is the result of the exponentialU(J) relationship. Based on thisU(J) law, the local pinning potential is determined to beUp(x)=U0(x/x0)[1−ln (x/x0)]. The voltage–currentE(J) resulting from the observedU(J) relationship, as well as the role of the Y2BaCuO5(211) phase in zone‐melted YBCO is discussed. ©1995 American Institute of Physics.