Aim The aim of this study was to comprehensively examine oxygen uptake (V̇O2) kinetics during cycling through mathematical modeling of the breath-by-breath gas exchange responses across eight conditions of unloaded cycling to moderate to high intensity exercise Methods Following determination of GET and V̇O2peak, eight participants (age: 24±8y; height: 1.78±0.09m; mass: 76.5±10.1kg; V̇O2peak: 3.89±0.72 L.min-1) completed a series of square-wave rest-to-exercise transitions at; -20%∆ (GET minus 20% of the difference in V̇O2 between that at GET and VO2peak), -10%∆, GET, 10%∆, 20%∆, 30%∆, 40%∆ and 50%∆. The V̇O2 kinetic response was modelled using mono- and bi-exponential non-linear regression techniques. Difference in the standard error of the estimates (SEE) for the mono- and bi-exponential models, and the slope of V̇O2 vs time (for the final minute of exercise), were analysed using paired and one-sample t-tests, respectively. Results The bi-exponential model SEE was lower than the mono-exponential model across all exercise intensities (p<0.05), indicating a better model fit. Steady-state V̇O2 was achieved across all exercise intensities (all V̇O2 vs. time slopes; p>0.05). The modelled slow component time constants, typical of literature reported values, indicated that the V̇O2 kinetic response would not be completed during the duration of the exercise. Conclusion It was shown that the addition of the more complex bi-exponential model resulted in a better model fit across all intensities (notably including sub-GET intensities). The slow component phase was incomplete in all cases, even when investigation of slopes indicated that a steady state had been achieved.