A hybrid brush seal is provided for sealing a circumferential gap between two machine components that are relatively rotatable with respect to each other having seal bristles mounted in a ring shape on a first machine component with bristle ends directed at the sealing surface of the second, rotating machine component. The bristle ends are kept from direct contact with the rotating machine component via one or more shoes which create a non-contact seal with the rotating machine component which is enhanced by the imposition of one or more spring elements connected between the machine component and shoes.