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The human oxygen uptake (V̇o 2 ) response to step-like increases in work rate is currently modeled by a First Order System Multi-Exponential (FOME) arrangement. Because of their first-order nature, none of FOME model’s exponentials is able to model an overshoot in the oxygen uptake kinetics (OV̇o 2 K). Nevertheless, OV̇o 2 K phenomena are observed in the fundamental component of trained individuals’ step responses. We hypothesized that a Mixed Multi-Exponential (MiME) model, where the fundamental component is modeled with a second- instead of a first-order system, would present a better overall performance than that of the traditional FOME model in fitting V̇o 2  on-kinetics at all work rates, either presenting or not OV̇o 2 K. Fourteen well-trained male cyclists performed three step on-transitions at each of three work rates below their individual lactate thresholds’ work rate (WR LT ), and two step on-transitions at each of two exercise intensities above WR LT . Averaged responses for each work rate were fitted with MiME and FOME models. Root mean standard errors were used for comparisons between fitting performances. Additionally, a methodology for detecting and quantifying OV̇o 2 K phenomena is proposed. Second order solutions performed better ( P &lt; 0.000) than the first-order exponential when the OV̇o 2 K was present, and did not differ statistically ( P = 0.973) in its absence. OV̇o 2 K occurrences were observed below and, for the first time, above WR LT  (88 and 7%, respectively). We concluded that the MiME model is more adequate and comprehensive than the FOME model in explaining V̇o 2  step on-transient responses, considering cases with or without OV̇o 2 K altogether.    NEW &amp; NOTEWORTHY To our knowledge, this is the first study applying second-order system equations to model V̇o 2  on-kinetics, which is useful for both mathematical representation and physiological understanding of the overshoot phenomenon manifesting in the fundamental components of some step responses. Moreover, an objective methodology for detecting and quantifying this overshoot that considers data from the whole response is proposed. Finally, this is the first work detecting overshoot occurrences outside the moderate domain of exercise.

Second-order modeling for the pulmonary oxygen uptake on-kinetics: a comprehensive solution for overshooting and nonovershooting responses to exercise