Michaelis-Menten equation is one of the best known mathematical theories in biochemistry. Its standard derivation is based on a simple treatment in terms of singular perturbation. Recent experimental developments in enzymology have made it possible that to study one enzyme molecule at a time. Thus a more realistic model for single-molecule enzymology is stochastic.

I shall present (1) classic singlar perturbation treatment (a la J.D. Murray and Lee & Segel), (2) single enzyme based stochastic model, (3) a semi-Markov formalism to enzyme kinetic which yields some new mathematical results, and (4) a singular perturbation treatment of systems with small number of enzymes. The relations between (1), (2) and (4) will be discussed.