A prototype kinetic model of bacterial glycolysis is formulated and a minimal set of assumptions is postulated that allows the formulation of an approximate mathematical model. To establish a baseline for future investigations of more complicated situations, we assume here that enzyme activities depend only on the concentrations of their substrates and that the cells are not growing. Under these circumstances, steady states of the glycolytic system are described by three coupled non-linear equations. The values of the kinetic parameters which give rise to steady-state multiplicities are examined, and conditions for multiplicity are derived. The analysis indicates that up to 10 steady states can exist for some parameter values.