A method for implanting a valve prosthesis at a native cardiac valve complex of a subject comprises implanting a distal fixation member of the valve prosthesis downstream of a native valve of the native valve complex such that two or more engagement arms of the distal fixation member apply, to a downstream side of the native valve, a first axial force directed upstream. The method also comprises implanting a proximal fixation member of the valve prosthesis at least partially upstream of the native valve, such that the proximal fixation member applies, to an upstream side of the native valve, a second axial force directed downstream, such that application of the first and second forces couples the valve prosthesis to the native valve complex. The engagement arms and the proximal fixation member capture leaflets of the native valve therebetween without folding over leaflets of the native valve.
