The hearing-aid interconnection system has a skin-penetrating hearing-aid abutment (2) and a fixture (4) anchored in a skull bone (6). A first press fit is formed between a first contact surface (8a) of the abutment and a first fixture contact surface (10a) of the fixture. The first abutment contact surface extends around the first fixture contact surface. A second press fit is formed between a second contact surface (8b) of the abutment and a second fixture contact surface (10b) of the fixture. The second fixture contact surface extends around the second abutment contact surface.