The stability of steady states and dynamic behaviors in a diauxic growth process were studied in a continuous culture with a mixed substrate. The stability of steady states was analytically discussed based on the eigenvalues using the authors’ previously proposed diauxic model. The number and stability of steady states appeared to vary with operational conditions such as dilution rate and feed substrate concentrations. The steady states can be classified into three categories : (i) a steady state where both substrates were consumed, (ii) a steady state where only one substrate was consumed and (iii) washout. To achieve a stable steady state where both substrates are consumed, the manipulated variables such as feed substrate concentration and dilution rate can be selected within a comparatively large area of values : dilution rate (0 to 0.7 h(-1)) against feed maltose concentration (0 to 1 g/l) in the case of feed glucose concentration (0.3 g/l) and against feed glucose concentration (0 to 1 g/l) in the case of feed maltose concentration (0.7 g/l). In the experiment involving a step change from a batch culture to a continuous culture, not only the dilution rate but also the amount of inducible enzyme in the cells was closely connected to the consumption of the two substrates in a continuous culture. The dynamic behaviors of cell concentration and substrate concentrations in the case of large step changes in feed concentrations were also examined under several operational conditions.