High‐spin states have been studied in72,73Kr using40Ca+40Ca and36Ar+40Ca reactions at 160, 164 and 145 MeV respectively. The properties and configurations of the bands observed are interpreted with the aid of unpaired cranked Nilsson‐Strutinsky/ cranked relativistic mean‐field calculations and paired total routhian surface and cranked relativistic Hartree‐Bogoliubov calculations. In73Kr the three previously known structures have been extended to a spin of ∼30ℏ and a fourth structure, which is believed to be the signature partner to the g9/2band, has been identified. The negative parity bands show evidence for an unusual type of band crossing. It is currently unclear whether this is a consequence of T=0 n‐p pairing. At the highest spins the unpaired calculations can reproduce the observed data, suggesting that there is little evidence for pairing correlations in this spin regime. In72Kr a new band has been identified that has the properties expected from the missing doubly aligned S‐band configuration. The properties of this band can be reproduced by the unpaired CNS/ CRMF calculations, again suggesting that the structure has little pairing. However, paired calculations appear to be necessary to reproduce the properties of the previously known structure in this nucleus. The72Kr results are also compared with projected shell model calculations. © 2003 American Institute of Physics