This paper is concerned with a mathematical analysis of the modified Guggenheim procedure. Theorems concerning the solutions of the differential equations which describe the general reaction $$E + SB\xrightarrow{{k_2 }}C + X, C\xrightarrow{{k_3 }}E + D$$ are derived and are used in a general discussion of the validity of the procedure. Numerical results are given to illustrate the general assertions and to obtain the range of values ofE 0 andS 0 for which the procedure is valid and enzymatic reaction such as α-chymotrypsin.