A flexible connection unit (284; 294; 296) for use in a bone stabilization device, where the flexible connection unit is sized and configured to be surgically implanted into the human body adjacent the spine and held in place by at least a first and a second bone coupling assembly that are anchored into a first and second vertebra, respectively, comprising: (a) a first rigid portion having an outer surface configured to be within and coupled to the first bone coupling assembly; (b) a second rigid portion; (c) a flexible member located between the first and the second rigid portions, the flexible member having an outer surface; (d) a spacer (288; 297) comprising: a rigid portion having an inner bore extending the length of the spacer rigid portion, the flexible member extending through the inner bore of the spacer rigid portion such that the spacer rigid portion can slide along the outer surface of the flexible member, and where the spacer rigid portion has an outer surface configured to be within and coupled to the second bone coupling assembly; characterized In that the spacer (288; 297) further comprises: - a first, compressible elastomeric portion located between the first rigid portion and the spacer rigid portion and having an inner bore extending the length of the first elastomeric portion with the flexible member extending through the bore of the first elastomeric portion; and - a second, compressible elastomeric portion located between the second rigid portion and the spacer rigid portion and having an inner bore extending the length of the second elastomeric portion with the flexible member extending through the bore of the second elastomeric portion; whereby the first and second elastomeric spacer portions permit and limit the sliding of the spacer rigid portion along the flexible member. (a) a first rigid portion having an outer surface configured to be within and coupled to the first bone coupling assembly; (b) a second rigid portion; (c) a flexible member located between the first and the second rigid portions, the flexible member having an outer surface; (d) a spacer (288; 297) comprising: a rigid portion having an inner bore extending the length of the spacer rigid portion, the flexible member extending through the inner bore of the spacer rigid portion such that the spacer rigid portion can slide along the outer surface of the flexible member, and where the spacer rigid portion has an outer surface configured to be within and coupled to the second bone coupling assembly; characterized In that the spacer (288; 297) further comprises: - a first, compressible elastomeric portion located between the first rigid portion and the spacer rigid portion and having an inner bore extending the length of the first elastomeric portion with the flexible member extending through the bore of the first elastomeric portion; and - a second, compressible elastomeric portion located between the second rigid portion and the spacer rigid portion and having an inner bore extending the length of the second elastomeric portion with the flexible member extending through the bore of the second elastomeric portion; whereby the first and second elastomeric spacer portions permit and limit the sliding of the spacer rigid portion along the flexible member. a rigid portion having an inner bore extending the length of the spacer rigid portion, the flexible member extending through the inner bore of the spacer rigid portion such that the spacer rigid portion can slide along the outer surface of the flexible member, and where the spacer rigid portion has an outer surface configured to be within and coupled to the second bone coupling assembly; - a first, compressible elastomeric portion located between the first rigid portion and the spacer rigid portion and having an inner bore extending the length of the first elastomeric portion with the flexible member extending through the bore of the first elastomeric portion; and - a second, compressible elastomeric portion located between the second rigid portion and the spacer rigid portion and having an inner bore extending the length of the second elastomeric portion with the flexible member extending through the bore of the second elastomeric portion; whereby the first and second elastomeric spacer portions permit and limit the sliding of the spacer rigid portion along the flexible member.