An implant (1) has attachment and hole-insert parts (2, 3) with an outer surface or outer surfaces having external layer arrangements (6, 7). The implant can be provided in a known manner with threads (3a, 3b) on cylindrical and conical portions. The implant is made in principle in two production stages. In a first production stage, the outer surface or outer surfaces (6a) of the implant are given a relatively high roughness value and/or a relatively high degree of porosity. In a second stage, the uneven or porous surface thus obtained is coated with an oxide layer (7) which can be uniform or can have different thicknesses along the longitudinal and/or circumferential directions(s) of the implant. In one embodiment, the oxide layer (7) can be coated with a bone-growth agent or bone-growth-promoting agent and/or calcium phosphate (16), for example by means of chemical deposition, dipping or sputtering.