The effect of relaxing quenched impurities on the dynamics are studied on the basis of a kinetic Ising model. In the model considered, the impurities affect the dynamics, but do not change the free energy or the value of Tc. It is shown that the critical exponents of the characteristic times of the spatial-correlation and autocorrelation functions are identical to those of the pure system. The amplitudes of the singularities depend, however, on the concentration and activation energy of the hopping impurities. This property may give rise to an extremely narrow central peak. The physical origin of the critical slowing-down of the disordered and pure system is identical however. © 1977 The American Physical Society.