The D’yakov work which deals with a shock that undergoes a slight disturbance is re−examined. Under a linear analysis the growth of perturbations is examined and this produces inequality restrictions for the shock to be stable. It is found that the shock is unstable for j2(dv/dp)H 〈−1 and j2(dv/dp)H〉 1 + 2M, where M is the Mach number of the shock with respect to the material behind, and −j2 is the slope of the Rayleigh line. These inequalities agree with those of D’yakov. It is also shown that these results are exactly the same as those derived by Erpenbeck by a different analysis. Some properties of general Hugoniot curves are also presented. It is demonstrated that the restriction to M<1, by itself, does not restrict the range of values for the slope of the Hugoniot curve.