The capacity of computational multiple steady states in a complex biochemical reaction networks, consisting of nine non-linear ordinary differential equations, was investigated. The system involved the production Of L-DOPA (L-3,4-dihydroxyphenytalanine) using L-tyrosine as a substrate and using the enzyme tyrosinase as the biocatalyst operating in an isothermal continuous stirred tank reactor (CSTR). A Deficiency One Algorithm and a Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states were constructed for three cases. The phenomena of hysteresis and bifurcation were discussed. Two sets of signatures of multiple steady states were provided, which could be used to identify reaction mechanism if steady states of some species had been measured. The capacity of multiple steady states was extended to its family members. (C) 2004 Elsevier Ltd. All rights reserved.