A valve device is provided for implantation at the location of a natural heart valve, for replacing the functioning of the natural heart valve. The valve device includes a holding structure and a plurality of leaflets that open and close as the heart beats and pressure changes. The valve device holding structure may comprise a substantially ring- shaped first section, or ventricular ring, and a substantially ring-shaped second section, or atrial ring, connected together by a connector. The valve device holding structure, which may include all parts besides the leaflets themselves, may be formed from a wire or tube made of a suitable flexible material that allows the valve device to be substantially straightened to a low profile in a constrained delivery condition and that allows the valve device to self-expand to its ring-shaped expanded profile when unconstrained during implantation.
