Cu–Al–Be β1′ martensite exhibits different levels of stabilization after various heat treatments (direct quenching into martensite, step-quenching, air cooling). However, this stabilization does not demonstrate time dependence upon martensite ageing at around room temperature, and can be considered as instantaneous. Cu–Al–Be martensite also stabilizes as a result of deformation of martensite starting from rather low values of prestrain. The conclusion is drawn that Cu–Al–Be alloy exhibits purely “mechanical” stabilization both after heat treatments and upon plastic deformation due to jamming the motion of interfaces. Non-elastic accommodation of transformation strain under a combined action of transformation stress and residual thermal stresses during the first direct martensitic transformation (MT), and “kinetic” stabilization due to sweeping-up of quenched-in defects during the martensitic transformation are considered as possible mechanisms of the observed instantaneous stabilization registered after heat treatment.