We use reaction network theory and stability analysis of nonlinear dynamical systems to construct and analyze a general compartmental model for the carbon-nitrogen (CN) metabolism of cyanobacteria in a flow-through photobioreactor. The model is aimed at simulating and elucidating ultradian oscillations of approximately 10 to 15 h, which were experimentally observed earlier under constant environmental conditions. Such cycles are assumed to be based solely on metabolism without involvement of both external (light/dark alteration) and internal (circadian clock) cues. We have taken an earlier simple 5-variable model of the CN metabolism, analyzed its potential for oscillatory dynamics under constant light and modified/extended it so that the new 13-variable model displays cyclic behavior quite closely simulating the experimental ultradian cycles. In addition, the model includes relevant external variables and parameters, such as dilution rate, concentrations of CO \(_2\) , N \(_2\) and biomass in the reactor, composition of the CO \(_2\) -enriched air bubbled through the reactor and the volumetric mass transfer coefficient expressing the intensity of bubbling. The methods of analyzing the model include stability analysis on two levels, (i) the reaction network (internal) level, whereby plausible rate coefficients are determined by a constrained stoichiometric optimization, and (ii) stability and bifurcation analysis of the entire model including external part. The outlined methods prove to be well suited for nonlinear bioprocesses obeying stoichiometry and kinetic rate laws.