NiTi alloys with different transition temperature sets M_s, T_R and A_f are considered here to be affected by cycling between the martensite and the parent phase. In alloys with a starting temperature M_s higher than 50 degrees C, M_s can shift on cycling below the critical temperature T_R at which a transition to the rhombohedral (R) phase appears. Alloys with M_s<<T_R do not suffer this shift of M_s on thermal cycling. Cycling strengthens all the alloys examined. Processing factors can modify both the initial transformation temperatures and the cycling behaviour.