The authors studied states of liquid sessile drops on a stretchable inclined elastic substrate to find out peculiarities of the contact angles hysteresis by digital optical microscopes. The drop elongation and contact angles were recorded on the stages of the band stretching and contraction. An anomalous behavior of the drop was found on the first step of the contraction during which the measured drop parameters remained unchanged. Finally, a new hydrophysical effect was found. It is hysteresis of the drop states, on the background of which the contact angle hysteresis exists.