Biological reduction of nitrate and nitrite was studied with a continuously operated cyclic reactor. The medium was fed to the reactor during the first phase of the cycle, and the effluent was drawn from the reactor during the third phase of the cycle; reaction occurred throughout the cycle. The process was described mathematically based on kinetic expressions revealed in an independent study. The model equations were subjected to detailed analysis with numerical codes based on the bifurcation theory for forced systems. The analysis has shown that in the operating parameter space there are extensive regions where the system can reach up to three different periodic states. The results of this analysis are shown in the form of two-dimensional operating diagrams. Numerical results have also shown that under certain operating conditions nitrate can be completely eliminated, while nitrite remains practically untreated. An experimental unit was designed, constructed, and used in experiments with a strain of Pseudomonas denitrificans [American Type Culture Collection (ATCC) 13867] under different operating conditions. The experimental results confirmed the theoretical predictions both qualitatively and quantitatively. Conditions under which complete reduction of both nitrate and nitrite is achieved, were found and experimentally verified. The results of this study suggest a methodology for analysis and design of cyclically operated bioreactors employed in denitrification of wastewaters.