The invention relates to a heart valve prosthesis for percutaneous replacement of a tricuspid valve including a stent-type support structure and a biological heart valve; the stent-type support structure can autonomously expand from a radially compressed state into a radially expanded state and includes a fluid-tight cover which extends like a tube over at least some portions of the support structure; the heart valve is arranged in a lateral opening in the support structure. Embodiments further relate to a system including a heart valve prosthesis of said type.