A compliant support for an axial thrust air bearing between a shaft and a housing with an annular thrust runner extending radially from the shaft having a runner bearing surface. The housing has a housing bearing surface and an air inlet in communication with a source of pressurized air. An annular foil support sleeve is disposed on the housing bearing surface, having an air foil surface with an array of foils. The foils serve to conduct air from the air inlet forming a pressurized air curtain between the runner bearing surface and foils on the the sleeve and is then disposed of through an air outlet. The sleeve has a compliant surface with at least one compliant annular ring. The compliant surface includes at least one compliant annular ring such as a fluorocarbon O-ring for low temperature service under 300.degree. F.; a fluorosilicon O-ring for mid-range temperature service 300-600.degree. F.; or a metallic mesh ring for high temperature service over 600.degree. F.
