Pseudoelasticity caused by pseudotwinning in short-range ordered In-Pb alloys (6, 8 and 11.6 at. % Pb) is studied in the temperature range 0.48–180 K. The mechanical hysteresis parameters, namely, the thermodynamic stress τT which provides the reversibility of plastic deformation and the frictional stress τf which characterizes the resistance offered by crystal lattice and its defects to twin boundaries motion are estimated. It is found that athermal processes determine the reversible deformation: the mechanical parameters τT and τf do not depend on temperature and strain rate. The stress τT increases and the stress τf decreases with increasing Pb content. One of the main conditions of the exhibition of superelasticity is the fulfillment of the inequality τT>τf.