Abstract: In the present paper, the method of matched asymptotic expansions is introduced to the Davis' viscous shock layer theory, and the result of the first order of approximation leads to the same hypersonic chemically reacting viscous shock layer equations as with the Davis' method. Although the resulting equations are the same, the fundamental assumptions of the latter method is more restricteived. The result of the second order approximation given for me first time in the present paper leads to a theoretical m...