The present invention is related to an intervertebral stabilizing device structured to connect two adjacent vertebrae. The device includes an upper stop element engageable with an upper vertebra and a lower stop element engageable with a lower vertebra. The stop elements include mutual support surfaces adapted to allow a mutual rotation of the upper and lower vertebrae about the patient's transverse and sagittal axes and to prevent a mutual rotation of the two vertebrae about a vertical axis. The support surfaces are further adapted to allow mutual translation of the vertebrae in a single direction along the sagittal axis and to allow translation between the two vertebrae in both directions along a vertical axis. Additionally, the support surfaces are also adapted to prevent translation between the two vertebrae in both directions along the transverse axis.