A bone fixation device comprises a plurality of brackets (6, 8, 42-48), each defining a surface formed with at least one recess (56, 58). Part of a ball (12-18, 52, 54) is mounted in each recess with an exposed face formed with a groove (24, 26, 52, 54) for receiving a fixation rod or bone screw. The brackets are capable of being brought together such that at least one pair of exposed ball faces are in juxtaposition with the grooves defining a sleeve for a fixation rod or bone screw, and means (10, 50) are included for urging the brackets and the exposed ball faces towards each other to clamp a fixation rod or bone screw between a pair of juxtaposed ball faces. Normally, the recesses and ball parts are arranged such that as the brackets are brought together at least two pairs of ball parts are in juxtaposition, forming two sleeves for fixation rods or bone screws.
