An influence of Cd content on the kinetics of a spontaneous low-temperature structure transformation in In-rich In - Cd alloys has been investigated using acoustic, resistivity and DSCtechniques. It is established that increase of the concentration of Cd leads to an essential increase of a driving force of the transition that results in an increase of the transition rate and in decrease of the relaxation time. The low-temperature instability of acoustic, resistivity and thermal properties is caused presumably by a decomposition of the solid solution that has features of a phase transition of the 1st order. The main empirical activation parameters of the transformation are derived. The activation energy amounts to U0 = 0.43 eV, the attempt period is τ 0 =5 × 10-9 s. The probable border of the decomposition in the phase diagram of the In-Cd system is established.