A fixation implant tightly secures ligament transplants and the like on or in bone tissue. The fixation implant has an elongate body, which has a front end for application and includes at least in some areas an expandable material which, after the implantation, exerts an expansion pressure on a surrounding bone substance. The body has an outer wall, which is provided at least in some areas with profiles extending substantially transverse to the longitudinal extent. The body is provided at its rear end with an engagement means for an insertion instrument, or it has an opening into a central recess for an expansion body. The expandable material is arranged substantially along the entire longitudinal extent of the body. The expandable material can exert pressure on the profiled areas in such a way that the external diameter of the body increases.