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 forj2(dv/dp)H⟨−1 andj2(dv/dp)H⟩ 1 + 2M, whereMis the Mach number of the shock with respect to the material behind, and −j2is 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 toM<1, by itself, does not restrict the range of values for the slope of the Hugoniot curve.