We present a model for the study of the effect of rheological hysteresis on compaction in sedimentary basins, when surface loading and unloading occurs. When compaction is slow (sedimentation rate is large and/or permeability is small), the hysteresis has little effect on the basal compaction layer, but in the more realistic case where compaction is fast (i.e., sedimentation is slow and/or permeability is large), surface unloading leads to downward propagation of a decompaction front, across which the vertical porosity gradient jumps, while subsequent surface reloading leads to downward propagation of a discontinuity in porosity, despite the fact that the porosity is governed by a diffusive equation of Richards type.