The effects of using different algorithms to estimate the time constant of changes in oxygen uptake at the onset of square-wave 120 W cycloergometric exercise were evaluated in seven subjects. The volume of oxygen taken up at the alveoli (VO(2Ai)) was determined breath-by-breath (BB) from the volume of O(2) transferred at the mouth (VO(2mi)) minus the corresponding volume changes in O(2) stores in the alveoli: VO(2Ai)= VO(2mi)-[V(Ai-1)(FO(2Ai)- FO(2Ai-1))+ FO(2Ai) x Delta V(Ai)], where V(Ai-1) is the alveolar volume at the end of the previous breath, FO(2Ai) and FO(2Ai-1) are estimated from the fractions of end-tidal O(2) in the current and previous breaths, respectively, and Delta V(Ai) is the change in volume during breath i. These quantities can be measured BB, with the exception of V(Ai-1) which must be assumed. The respiratory cycle has been defined as the time elapsing between identical fractions of expiratory gas in two successive breaths. Using this approach, since FO(2Ai)= FO(2Ai-1), any assumption regarding V(Ai-1) becomes unnecessary. In the present study, VO(2Ai) was calculated firstly, by using this approach, and secondly by setting different V(Ai-1) values (from 0 to FRC+0.5 l, where FRC is the functional residual capacity). Values for alveolar O(2) flow (VO(2Ai)), as calculated from the quotient of VO(2Ai) divided by breath duration, were then fitted bi-exponentially. The time constant of the phase II kinetics of VO(2Ai) (tau(2)) was linearly related to V(Ai-1), increasing from 36.6 s (V(Ai-1)=0) to 46.8 s (V(Ai-1)=FRC+0.5 l) while tau(2) estimated using the first approach amounted to 34.3 s. We concluded that, firstly, the first approach allowed us to calculate O(2A) during transitions in step exercise; and secondly, when using methods wherein V(Ai-1) must be assumed, tau(2) depended on V(Ai-1).