(1) A functional and comparative study has been made of the jaw mechanisms of representatives of the major classes of arthropods, covering, where appropriate, the whole endoskeletal systems of the head and the form and function of other mouth parts, hypopharynx, etc. (2) Mandibles are developed embryologically, and presumably phylogenetically also, in one or other of two ways. Type A, in which the biting structures are developed from a proximal endite or gnathobase (Crustacea, Chelicerata), and type B, in which the mandible is developed from a whole limb, the tip of which and not the base is used for gnathal purposes (Onychophora, Myriapoda, Hexapoda). (3) Two types of movement typical of the more primitive ambulatory trunk limbs have been exploited in mandibular evolution. Type I mandibular movement uses the promotor-remotor swing of an ambulatory or swimming coxa on the body, but the axis of swing may be shifted in various ways (Crustacea, Thysanura), and type II mandibular movement uses the prehensile action in the transverse plane of a coxa or coxa and telopodite. Type II is found in Myriapoda, where segmentation of the whole-limb mandible is essential, and direct transverse gnathobasic biting is employed by Limulus. Mandibles of types I and II appear to have evolved independently in the named examples. (4) The more primitive examples of type II mandibles suit fine food feeding and the scratching of food surfaces. The gape is small, biting, if any, is weak, and added hydraulic efficiencies enable fine particles to be sucked up by terrestrial types (Chirocephalus,Hemimysis,Paranaspides,Petrobius). (5) Biting in the transverse plane is not a primitive attribute of the Arthropoda outside the Chelicerata and certain Myriapoda. In the more primitive Crustacea and Hexapoda transverse biting is absent and there is little basic adduction and abduction. Transverse muscles primarily serve promotor-remotor rolling movements. No example has been found of a so-called monocondylic mandible of a crustacean or of a hexapod which exhibits freedom of movement in all directions from this point and a basic power of transverse adduction, whether or not the mandible possesses a formed dorsal articulation. (6) Strong biting in the transverse plane suiting hard or large food is a repeated end term in arthropodan evolution. The examples considered are: some Decapoda, Peracarida, Pterygota, Diplopoda and Symphyla. Adduction in the transverse plane is mechanically simple, but abduction presents great problems, hitherto not appreciated, which have had to be resolved by every group of animals attempting to evolve such mandibles. The resolutions of the difficulty are various, mutually exclusive, and independently evolved by mandibles of all types. (7) The feeding mechanism ofLimulusis described. The jaw mechanisms ofLimulusand of Crustacea are fundamentally different and have probably been evolved in independence. (8) The validity of the evidence for the existence of a pre-coxal segment in Xiphosura needs reconsideration. (9) The rolling whole-limb mandibles ofPetrobiusarenot far removed from a central type which could have given rise to the various mandibles occurring throughout the Hexapoda. It is shown in some detail how this mechanism is parallel to but different from that of the rolling gnathobasic mandibles of the more primitive Crustacea. Differences between the mandibles of Hexapoda and Crustacea concern mandibular form, musculature, movement and derivation; the head endoskeleton, and the form and movements of maxilla 1 are also different. The superficial resemblances are considered to be due to convergence between mandibles of unlike origin which utilize the same type of movement of an ambulatory limb. (10) Present-day animals show how thePetrobius-type of jaw mechanism could have given rise to (i) the strong transverse biting of the Lepismatidae and Pterygota with loss of hydraulic efficiency of the Petrobius type and to (ii) a further development of the rolling movement, together with protrusibility of mandibles, which has been made possible by entognathy in the Apterygota. These two trends are mutually exclusive. (11) Entognathy is a condition permitting great proximal mobility of the mandible and hence confers the powers of mandibular protrusion which are absent in strong closely articulated mandibles. Entognathy in essentially similar form, but differing in details, has been evolved in Onychophora, Chilopoda, Pauropoda, Collembola, Diplura and Protura. The ‘Entognatha’ is not considered to be a valid taxonomic group but one of convergence. (12) A basic pattern of: mandibular structure, musculature, movements, associated head endoskeleton, and of the structure and movements of maxilla 1 is recognizable throughout the less specialized Pterygota, Thysanura, Collembola and Diplura, so linking these groups together by characters having nothing to do with the possession of three pairs of legs. This basic pattern of mandible and maxilla 1 is not found in the Myriapoda. (13) A unified system of skeletal tendons and apodemes exists within the Arthropoda which has hitherto been imperfectly described. Anterior and posterior tentorial apodemes are present throughout the less specialized of the Hexapoda in essentially similar form. The segmental tendon system, present embryologically in all body segments in many animals, occurs in the adult hexapod head except where strong transverse biting has been evolved, and its presence then is consequently not required. Hexapod-like tentorial apodemes are absent in Crustacea, but homologous anterior tentorial apodemes are present in Myriapoda where their mobility is enhanced. Rigidity of tentorial apodemes is found in hexapods where strong transverse biting has been evolved (Pterygota). (14) The details of the feeding mechanism of a chilopod are described. The mandibular mechanism has clearly been derived from the same basic transversely moving mandibles of the type seen in Diplopoda and Symphyla, but modified by the development of entognathy to give a highly specialized mechanism suiting carnivorous feeding and crevice living, and not found in any other group. (15) The Chilopoda, Diplopoda and Symphyla all appear to have obtained direct transverse biting without any preliminary rolling mandible such as seen in Thysanura, but segmentation of their mandibles is essential. All have used the mobility of the anterior tentorial apodemes to provide (Diplopoda) or enhance (Symphyla and Chilopoda) the abductor force which opens the jaws. The differences between the mandibular mechanisms of Chilopoda, Diplopoda and Symphyla indicate independent evolution from a common type and no one of these three classes could readily give rise to the mandibular mechanisms present in either of the other two. The term Myriapoda, indicating affinity between Chilopoda, Diplopoda, Symphyla and Pauropoda deserves to be reinstated. (16) The symphylan mandibular mechanism, together with the structure and use of maxilla 1, the mobility of the anterior tentorial apodeme, and the presence of the myriapodan maxilla 1 salivary gland, are so entirely opposed both to the thysanuran condition and to the directions of evolutionary change seen in the Pterygota and entognathous Apterygota (whose basis appears to lie in the Thysanura) as to make the symphylan theory of insect origin untenable. (17) It is concluded that jaws have evolved independently in (i) the Chelicerata, (ii) the Crustacea and (iii) the Onychophora—Myriapoda—Hexapoda series. Within the latter the jaws in the Onychophora must have evolved very early, before much cephalization had taken place. The mandibular mechanisms of the Myriapoda and Hexapoda are so differ ent as to indicate that there can be no close connexion between these two groups of classes apart from a very distant common origin. The parallel evolution of jaws in arthropods must date from the earliest differentiation of the major classes. The Mandibulata cannot be regarded as a related group, but the term may serve to indicate a Grade of advancement. The bearing of these results on taxonomic systems is discussed.