An intervertebral disk prosthesis system, which is used for forming an artificial intervertebral disk and comprises a first and a second prosthesis component wherein each of the two prosthesis components comprises a first and a second vertebral body contacting element for placement on neighboring vertebral bodies bounding an intervertebral disk space of a spinal column and a joint element that is mounted between and is moveable relative to at least one of the first and second vertebral body contacting elements, attains a substantially natural range of motion independent of the positioning of the two prosthesis components relative to each other and to the neighboring vertebral bodies. Each prosthesis component has a ball joint formed between the first and second vertebral body contacting elements.