The present invention relates to methods for enhancing the hemodynamicstability of an individual undergoing surgery by administering a compositioncomprising a hemoglobin-~based oxygen carrier. In one embodiment, the presentinvention relates to the use of polyalkylene oxide modified hemoglobins withreduced cooperativity and a high oxygen affinity to enhance oxygen offloadingas a preventative measure to avoid hemodynamic stability-related complicationsduring surgery.