A hybrid seal for sealing the circumferential gap between a first machine component and a second machine component comprises at least one shoe extending along one of the machine components in a position to create a non-contact seal, at least one spring element connected between one of the machine components and the shoe(s) and a stack of sealing elements located within a slot formed in the shoe(s), wherein a primary seal and secondary seal of the circumferential gap is created by the shoe(s) in cooperation with the spring element(s) and sealing elements, respectively.