The invention relates to intervertebral disc implants that imitate the natural freedom of movement and facilitate translational and/or rotational displacements of the intervertebral disc in relation to the base plate, independently of the possible displacements of the base plate in relation to the intervertebral disc. To achieve said displacements, the intervertebral disc is mounted on the base plate by means of the fixing elements located in the interior of the implant, in such a way that translational and/or rotational displacements can take place. In addition, the bearing surface between the top plate and the intervertebral disc is spherical, thus maximising the contact surface.