The purpose of this study was to compare critical velocity (CV) estimates from five mathematical models, and to examine the oxygen uptake (VO(2)) and heart rate (HR) responses during treadmill runs at the five estimates of CV. Ten subjects (six males and four females) performed one incremental test to determine maximal oxygen consumption (VO(2max)) and four or five randomly ordered constant-velocity trials on a treadmill for the estimation of CV. Five mathematical models were used to estimate CV for each subject including two linear, two nonlinear, and an exponential model. Up to five randomly ordered runs to exhaustion were performed by each subject at treadmill velocities that corresponded to the five CV estimates, and VO(2) and HR responses were monitored throughout each trial. The 3-parameter, nonlinear (Non-3) model produced CV estimates that were significantly (P < 0.05) less than the other four models. During runs at CV estimates, five subjects did not complete 60 min at the their estimate from the Non-3 model, nine did not complete 60 min at their estimate from the Non-2 model, and no subjects completed 60 min at any estimate from the other three models. The mean HR value (179 +/- 18 beats min(-1), HR(peak)) at the end of runs at CV using the Non-3 model was significantly less than the maximal HR (195 +/- 7 beats min(-1), HR(max)) achieved during the incremental trial to exhaustion. However, mean HR(peak) values from runs at all other CV estimates were not significantly different from HR(max). Furthermore, data indicated that mean HR(peak) values increased during runs at CV estimates from the third minute to the end of exercise for all models, and that these increases in VO(2) (range = 367-458 ml min(-1)) were significantly greater than that typically associated with O(2) drift ( approximately 200 ml min(-1)) for all but the exponential model, indicating a VO(2) slow component associated with CV estimates from four of the five models. However, the mean VO(2) values at the end of exercise during the runs at CV estimates for all five mathematical models were significantly less than the mean VO(2max) value. These results suggest that, in most cases, CV estimated from the five models does not represent a fatigueless task. In addition, the mean CV estimates from the five models varied by 18%, and four of the five mean CV estimates were within the heavy exercise domain. Therefore, CV would not represent the demarcation point between heavy and severe exercise domains.