The rod-shaped apatite crystals of the formula Ca.sub.5(PO.sub.4).sub.3(OH).sub.xF.sub.y have the following features a) the length-to-breadth ratio of the crystals is at least .gtoreq.5 and b) x+y=1, where if x or y.noteq.0 the total amount of the crystals is present as a mixture of individual hydroxyapatite crystals and fluoroapatite crystals and/or as mixed crystals, such that, based on the total amount of the crystals, (1-x)100% of the hydroxide ions present if y=0 are replaced by fluoride ions.The invention furthermore describes dispersions which contain such rod-shaped apatite crystals, and a process for the preparation of the dispersions or of the apatite crystals.