A wave-powered vehicle which comprises a float, a swimmer, and a tether connecting the float and the swimmer; the float, swimmer and tether being such that, when the vehicle is in still water, (i) the float is on or near the surface of the water, (ii) the swimmer is submerged below the float, and (iii) the tether is under tension; and the swimmer, when the vehicle is in wave-bearing water, interacting with the water to generate forces which tend to move the float in a direction having a horizontal component, characterized in that there is a single tether which comprises a cable which (a) has a cross-section which (i) has a chord length which is 1.3 to 7.6 cm (0.5 to 3.0 inch) and (ii) comprises a leading edge portion and a trailing edge portion, the leading edge portion including the greatest width of the cross-section, the greatest width being 0.3 to 2.5 cm (0.1 to 1.0 inch) and at most 0.5 times the chord length of the cross-section, and (b) comprises an elongate tensile member which carries load when the cable is under tension, at least one additional elongate member which does not carry load when the cable is under tension, and which comprises one or more of insulated electrical conductors, optical fibers and acoustic cables, and a jacket which provides the outer surface of the cable and which has been prepared by extruding or otherwise molding a polymeric composition around the elongate tensile member and the additional elongate member; the cable being aligned so that its leading-edge portion is directed towards the front of the WPV, and the WPV comprises means for determining when the tether is twisted. a float, a swimmer, and a tether connecting the float and the swimmer; (i) the float is on or near the surface of the water, (ii) the swimmer is submerged below the float, and (iii) the tether is under tension; there is a single tether which comprises a cable which (a) has a cross-section which (i) has a chord length which is 1.3 to 7.6 cm (0.5 to 3.0 inch) and (ii) comprises a leading edge portion and a trailing edge portion, the leading edge portion including the greatest width of the cross-section, the greatest width being 0.3 to 2.5 cm (0.1 to 1.0 inch) and at most 0.5 times the chord length of the cross-section, and (b) comprises an elongate tensile member which carries load when the cable is under tension, at least one additional elongate member which does not carry load when the cable is under tension, and which comprises one or more of insulated electrical conductors, optical fibers and acoustic cables, and a jacket which provides the outer surface of the cable and which has been prepared by extruding or otherwise molding a polymeric composition around the elongate tensile member and the additional elongate member; the cable being aligned so that its leading-edge portion is directed towards the front of the WPV, and (a) has a cross-section which (i) has a chord length which is 1.3 to 7.6 cm (0.5 to 3.0 inch) and (ii) comprises a leading edge portion and a trailing edge portion, the leading edge portion including the greatest width of the cross-section, the greatest width being 0.3 to 2.5 cm (0.1 to 1.0 inch) and at most 0.5 times the chord length of the cross-section, and (i) has a chord length which is 1.3 to 7.6 cm (0.5 to 3.0 inch) and (ii) comprises a leading edge portion and a trailing edge portion, the leading edge portion including the greatest width of the cross-section, the greatest width being 0.3 to 2.5 cm (0.1 to 1.0 inch) and at most 0.5 times the chord length of the cross-section, and (b) comprises an elongate tensile member which carries load when the cable is under tension, at least one additional elongate member which does not carry load when the cable is under tension, and which comprises one or more of insulated electrical conductors, optical fibers and acoustic cables, and a jacket which provides the outer surface of the cable and which has been prepared by extruding or otherwise molding a polymeric composition around the elongate tensile member and the additional elongate member; an elongate tensile member which carries load when the cable is under tension, at least one additional elongate member which does not carry load when the cable is under tension, and which comprises one or more of insulated electrical conductors, optical fibers and acoustic cables, and a jacket which provides the outer surface of the cable and which has been prepared by extruding or otherwise molding a polymeric composition around the elongate tensile member and the additional elongate member; the WPV comprises means for determining when the tether is twisted.