The failure of cut slopes in the overconsolidated Epirus blue marl led to the investigation and classification of its properties. The stress-strain curves of a sizable number of samples exhibited irregular behavior. The main type of irregularity was the existence of a stress plateau intermediate between the peak and the residual strength. The possible implications of this type of behavior on the mechanism of progressive failure of slopes are examined. The main conclusion is that it is possible that a slide may occur along the slip surface of an apparently stabilized previous slope failure while the shear strength is further reduced down to its final residual level.