A delivery catheter for implanting a self-expanding implant such as a cardiovascular implant. An outer catheter shaft is formed as an implant capsule for encasing the implant during delivery. A flexible distal support element having a substantially truncated cone-shaped portion, which tapers in the proximal direction, is attached, directly proximally of the implant, in a fixed position to a first, inner catheter shaft, and/or a flexible proximal support element having a substantially truncated cone-shaped portion, which tapers in the proximal direction, is inserted at the proximal end of the implant capsule into the second, outer catheter shaft in a fixed position.
