The constructional morphology of the jaw apparatus in the horn-shark Heterodontus has been investigated. The origines and insertions of the jaw muscles have been delimited and the lines of action were determined. The individual muscles have been weighed, in order to get on the basis of their masses an estimate of the forces which are exerted by the components of the jaw musculature. The mandibular joints, the occlusion of the jaws, morphological details of the upper and lower jaws as well as the "subodontium" have been subject to macroscopic and microscopic study. The joint between palatoquadrate and mandibular consists of a medial and a lateral compartment. Only hinge movements are possible. If the jaws are closed, the contacts between upper and lower jaws are confined to the large crushing teeth of only one or two tooth families. The teeth are fixed to the jaw cartilage by ligamentous structures. Three layers can be discerned histologically: The uppermost layer, beneath the bases of the teeth, is composed of the fibrae interdentales and of the fibrae subbasales. By these, the individual teeth are firmly connected to form a continuous pavement. - The middle layer is characterised by the great number of cell nuclei. - The fibre system which constitutes the lowermost layer is arranged according to its function. The subdental layer of fibrous tissue grows faster than the one adjacent to the jaws. Thus a particular growth structure is formed. - Two constructive principles are realised: 1. The biting forces or "loads", applied to one or two teeth, are split and distributed on all teeth of the same family which are lingual of the loaded one. 2. As in the thecodont mammals, the compressive biting (= occlusal) force is transformed into a tensile force by the tooth-fixing apparatus and by the shapes of the jaws and this is sustained by fibrous structures. Magnitude and directions of the stresses which appear in the upper and lower jaw during biting are compared with stress patterns evoked in consoles and in beams of technical constructions. The moments of resistence have been calculated for 9 or 8 cross sections, respectively, through the upper and the lower jaw. The forms of both jaws are comparable to a beam of equal strength on two supports, namely, bitten object and joints; while the load is represented by the muscular force. Where the bending moments are at a maximum, opposite to the muscle insertions, a strong ligamentous reinforcement of the perichondrium extends parallel to the tooth rows and fades out towards the joint and towards the symphysis. The strength properties of cartilage and of collagenous fibres in the species under consideration have been measured. The lines of action of the jaw muscles intersect in the area where the moments of resistence reach their maximum. The largest crushing teeth are located in this same section, so that the muscles exert most force on the teeth, while the joint is exposed to only moderate compression.