A prosthetic valve assembly for intraluminal implantation into a lumen of a patient for replacing a native deficient valve, the valve assembly comprising: an outer balloon expandable support having inextensible means and configured to be expanded radially beyond a smallest diameter defined by the inextensible means, for anchoring against a lumen wall of the patient and forming an inextensible waist section defined by said smallest diameter in the expandable support, a core valve support comprising a collapsible and self-expanding support ring configured to be anchored in the outer balloon expandable support once expanded, the support ring including a plurality of flexible posts upwardly extending from the ring and capable of moving radially inwardly, the core valve support being configured to be collapsed for intraluminal implantation and being configured to expand into the lumen and the outer balloon expandable support once the outer balloon expandable support is anchored against the lumen wall, the support ring including anchoring means for anchoring the support ring upwardly and downwardly to the inextensible waist section when the core valve support is anchored within the outer balloon expandable support and once the outer balloon expandable support is anchored against the lumen wall, and a plurality of flexible leaflets (44,45,46) pivotally connected to the collapsible and self-expanding support ring and posts and configured to move between an open position for permitting a blood flow through the valve assembly and a closed position for preventing a backflow through the valve assembly, wherein a gap is defined between the flexible posts and the balloon expandable support to prevent the posts and leaflets from entering into contact with the support during the movements between the open and closed positions. an outer balloon expandable support having inextensible means and configured to be expanded radially beyond a smallest diameter defined by the inextensible means, for anchoring against a lumen wall of the patient and forming an inextensible waist section defined by said smallest diameter in the expandable support, a core valve support comprising a collapsible and self-expanding support ring configured to be anchored in the outer balloon expandable support once expanded, the support ring including a plurality of flexible posts upwardly extending from the ring and capable of moving radially inwardly, the core valve support being configured to be collapsed for intraluminal implantation and being configured to expand into the lumen and the outer balloon expandable support once the outer balloon expandable support is anchored against the lumen wall, the support ring including anchoring means for anchoring the support ring upwardly and downwardly to the inextensible waist section when the core valve support is anchored within the outer balloon expandable support and once the outer balloon expandable support is anchored against the lumen wall, and a plurality of flexible leaflets (44,45,46) pivotally connected to the collapsible and self-expanding support ring and posts and configured to move between an open position for permitting a blood flow through the valve assembly and a closed position for preventing a backflow through the valve assembly, wherein a gap is defined between the flexible posts and the balloon expandable support to prevent the posts and leaflets from entering into contact with the support during the movements between the open and closed positions.