Low frequency internal friction of Ti49Ni51 binary and Ti50Ni40Cu10 ternary shape memory alloys has been measured. The effect of solution and aging heat treatments on the damping property was examined. The temperature spectrum of internal friction for TiNi binary alloy consists, in general, of two peaks; one is a transition peak which is associated with the parent-martensite transformation and is rather unstable in a sense that it strongly depends on the frequency and decreases considerably when held at a constant temperature. The other one is a very high peak of the order of 10-2, which appears at around 200K. It appears both on cooling and on heating with no temperature hysteresis, and is very stable. The behavior of the peak is strongly influenced by the heat treatments. The trial of two-stage aging with a purpose of improving the damping capacity has been proved unsatisfactory. TiNiCu has a very high damping, the highest internal friction reaching 0.2, but by quenching from very high temperature, say 1373K, the damping is remarkably lowered. For the realization of high damping the quenching from a certain temperature range around 1173K seems the most preferable condition.