The process of martensite stabilization is investigated by resistometric method and positron annihilation spectroscopy in Cu-Al-Zn and Cu-Al-Ni alloys exhibiting the shape memory effect. A strong stabilization of martensite observed in Cu-Al-Zn alloys is explained by diffusion of divacancies and monovacancies formed during quenching with the following values of the Arrhenius relation E-2V(M) = (0.69 +/- 0.02) eV, K-04 = 6.4 x 10(8.0+/-0.1) s(-1) and E-1V(M) = (0.84 +/- 0.02) eV, K-03 = 6 x 10(9.00+/-0.15) s(-1), respectively. It was found that the energy of vacancy formation in Cu-8.5Al-14.5Zn(%wt.) alloy was 0.56 eV. The proposed model has been confirmed by applying the positron annihilation technique. In Cu-Al-Ni alloys the disappearance of quenched-in vacancies is described by one recovery process only with the diffusion energy of monovacancy 0.74 eV.