Background The growth of Aspergillus awamori and Aspergillus oryzae in a self-designed, multi-stacked circular tray solid-state bioreactor (SSB), operating in solid-state fermentation (SSF) conditions at a laboratory scale, was studied. The bioreactor was divided into six layers by six circular perforated trays. Wheat bran was used as both a carrier of bound mycelia and nutrient medium for the growth of A. awamori and A. oryzae. The new tray SSB is equipped with instrumentation (an oxygen (O-2)/carbon dioxide (CO2) gas analyser and a thermocouple) to continuously monitor O-2 consumption and CO2 and heat evolved, which can directly be used to monitor the fungal biomass. The integrated Gompertz model was used to describe the accumulated evolution of CO2. Results The results from the models strongly suggest that the evolved and accumulated CO2 can be used to excellently describe fungal growth. Another important parameter that can be determined by the gas balance method is the respiratory quotient (RQ). This is the ratio of the CO2 evolution rate (CER) to the O-2 uptake rate (OUR). The use of CER and OUR confirmed that correlated measurements of microbial activity are available, and the determination of RQ may propose an explanation for differences from expected levels. The kinetic behaviour of the fungal culture, using raw CO2, which represents an accumulation term, was integrated with respect to time and fitted to a Gompertz model, a log-like equation. The model can be used to generate parameter values that may be used to verify the experimental data, and also to simulate and optimise the process. Conclusion Overall, A. awamori and A. oryzae have their own ability to degrade and utilise the complex compositions contained in the solid substrate, and fermentation conditions may lead to possible comparisons. In addition, multi-stacked circular tray SSB systems demonstrated an excellent system for further investigations of mass transfer and possibly for large-scale operation, though considerable optimisation work remains to be done; for example, the height/diameter ratio and total number of trays should be optimised.