The arrangement of the protein filaments and other details of the ultrastructure of the contractile apparatus have been studied by methods which include the examination of thin sections in the electron microscope. The results help towards a better understanding of three general problems: the reasons why some muscles appear striated and others smooth; the mechanism of contraction in muscles which are not cross-striated; and the mechanism by which certain muscles of molluscs can maintain a high level of tension for long periods without fatigue. The filaments are of two kinds, thick paramyosin filaments, and much thinner filaments which very probably contain mainly actin. Both are short, relative to the length of the fibre, lie parallel to the fibre axis, and are grouped into separate arrays which alternate with each other along the length of the fibre. The arrays partly overlap, and in the regions of overlap each thick filament is surrounded by twelve thin ones, and each thin filament is usually ‘shared' by two thick ones. The regions of the fibre where the arrays of thin filaments are exposed are identified as I -bands, the intervening regions (arrays of paramyosin filaments partly over-lapping with arrays of thin filaments) as A -bands. The relative positions of the arrays change with the length of the muscle: the extent of overlap in the A -bands increases as the muscle shortens and decreases on stretching. Thus the muscle shortens by a sliding filament mechanism. Although the muscle is identified as a striated muscle because it has A - and I -bands, it differs from cross -striated muscles in two respects. In the first place, the bands lie at a small angle (about 10°) to the fibre axis, and are arranged helically around the outer part of the fibre, giving rise to the ‘double-oblique striation’ visible in the light microscope; more over, the bands branch and anastomose with each other in the core of the fibre. In the second place, there are no Z -lines, but in the planes where Z -lines would be expected, discrete dense-bodies are present. Similar dense-bodies occur in many smooth muscles, for example, in the mammalian uterus (Mark 1956; Shoenberg 1958), and in the anterior byssus retractor of Mytilus (Hanson & Lowy 1959 a ). The contractile apparatus of the latter closely resembles that of the oyster muscle in many respects, but the filaments are not clearly grouped into separate arrays. This feature, the presence or absence of segregated arrays of filaments, could serve as the main criterion for distinguishing striated from smooth muscles. Where the arrays of thick and thin filaments overlap in the A -bands, the two kinds of filaments appear to be cross-linked by means of transverse projections which belong to the thick filaments. The view is put forward that the paramyosin filaments are comparable to the myosin-containing filaments of the cross-striated muscles of vertebrates, and that the cross-links in the oyster muscle are comparable to actin-myosin links. The role which paramyosin filaments play in the mechanism by which certain muscles of molluscs maintain tension very economically is also discussed. The results described in this paper support the hypothesis (Lowy & Millman 1959 b , 1960) that tension is held by cross-links in a sliding filament contractile mechanism and that the economy of the system is due to a low rate of detachment of these cross-links. The alternative ‘catch’-mechanism hypothesis (Johnson, Kahn & Szent-Györgyi 1959; Johnson & Szent-Györgyi 1959; Rüegg 1959) which supposes that tension is maintained by some change of state of the protein within a paramyosin system, is difficult to reconcile with the present findings. Structures which resemble the ‘dyads’ of the cross-striated muscles of vertebrates have been found beneath the cell membrane. Their possible function in the intracellular transmission of stimuli is discussed in view of the fact that the fibres of the oyster muscle are only about 2 μ thick.