We investigate the possible effects of local regions with an appreciably lowered anisotropy constant K on the magnetization reversal in hard magnetic materials. Within the framework of very simple model‐assumptions, and for different shapes of the defect‐regions, we calculate the critical fields for the growing of a reversed nucleus (Hn c) and for the pinning of an extended domain wall (Hp c). In particular, we investigate the dependence of Hn c on the form and size of the defect‐regions, on the spatial gradient of K, and on the angle ϑ between magnetic field and easy axis. For the appropriate 1‐dimensional geometry, the results are in reasonable agreement with Abraham and Aharoni’s exact micromagnetic calculations (ϑ=0). The variation of Hn c with the angle ϑ resembles the Kondorsky‐1/cosϑ behavior, and is markedly different from the predictions of the Stoner‐Wohlfarth theory for coherent rotation. Pinning of extended domain walls turns out to be important only for very large K‐gradients. The model‐calculations are compatable with recent experiments on RE‐Co systems.