We compared estimates for the phase 2 time constant (τ) of oxygen uptake (V˙O2) during moderate- and heavy-intensity exercise, and the slow component of V˙O2 during heavy-intensity exercise using previously published exponential models. Estimates for τ and the slow component were different (P < 0.05) among models. For moderate-intensity exercise, a two-component exponential model, or a mono-exponential model fitted from 20 s to 3 min were best. For heavy-intensity exercise, a three-component model fitted throughout the entire 6 min bout of exercise, or a two-component model fitted from 20 s were best. When the time delays for the two- and three-component models were equal the best statistical fit was obtained; however, this model produced an inappropriately low ΔV˙O2/ΔWR (WR, work rate) for the projected phase 2 steady state, and the estimate of phase 2 τ was shortened compared with other models. The slow component was quantified as the difference between V˙O2 at end-exercise (6 min) and at 3 min (ΔV˙O2 (6-3 min); 259 ml min-1), and also using the phase 3 amplitude terms (truncated to end-exercise) from exponential fits (409-833 ml min-1). Onset of the slow component was identified by the phase 3 time delay parameter as being of delayed onset ~2 min (vs. arbitrary 3 min). Using this delay ΔV˙O2 (6-2 min) was ~400 ml min-1. Use of valid consistent methods to estimate τ and the slow component in exercise are needed to advance physiological understanding. Experimental Physiology (2001) 86.5, 667-676.