A device for deploying a cardiac valve prosthesis includes at least one constraint member for radially constraining radially expandable annular portions of the valve. The constraint member is actuatable to release the annular formations constrained thereby and permit radial expansion of these annular formations. The constraint member has associated a first, slow-acting actuating mechanism and a second, fast-acting mechanism, adapted to produce relatively slow and fast release of the annular formations constrained thereby. The device may include a first constraint member and second constraint member in the form of telescoping sleeves. The slow-acting actuating mechanism will thus act on the outer sleeve, while the fast-acting mechanism will act on the inner sleeve to produce, respectively, slow and fast release of the annular formations.