The purpose of this study was to investigate to what extent aerobic power (MAP), maximal anaerobic power (MANP), anaerobic capacity measured as time to exhaustion at 130% MAP (TTE), and maximal accumulated oxygen deficit (MAOD) correlated with 800 m double poling time trial performance (800TT) in a ski ergometer. A second aim was to investigate the relationship between TTE and MAOD, and to what extent TTE and MAOD would relate to anaerobic power reserve (APR). Eighteen cross-country skiers were tested for peak oxygen uptake (VO2peak) and oxygen cost of double poling to assess MAP. Peak power measurements during a 100 m TT were performed to assess MANP. TTE and an 800TT with continuousVO2measurements were performed to assess time performance and MAOD. All tests were performed on a ski ergometer. Both MAP and MANP correlated strongly (r= − 0.936 and − 0.922, respectively,p< 0.01) with 800TT. Neither TTE nor MAOD correlated with 800TT. TTE correlated moderately with MAOD, both in mL kg−1and in %VO2peak(r= 0.559,p< 0.05 and 0.621,p< 0.01, respectively). Both TTE and MAOD seemed to be a product of APR. These results suggest focusing on MAP and MANP, but not anaerobic capacity to explain time performance in an event with approximately 3 min duration.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00421-023-05149-9.