The invention relates to an intervertebral implant comprising a spacer constituted by first and second parts (12, 14), said parts being provided with mutual assembly means comprising first clip-fastener means (54, 56) secured to one of said parts, second clip-fastener means (49, 50) secured to the other part and suitable for co-operating with the first clip-fastener means to achieve releasable clip-fastening between the two parts, and guide means for guiding the two parts (12, 14) during clip-fastening, said guide means being distinct from the clip-fastening means and comprising: a substantially non-deformable first guide assembly (42, 44) secured to one of said parts; and a substantially non-deformable second guide assembly (46, 48) secured to the other part to co-operate with the first guide assembly.