A rotary-oscillating sub-assembly (1; 101) for positive displacement pumping of a fluid, said sub-assembly comprising: a hollow body (2; 102) defining a cylindrical cavity (10; 110) of longitudinal axis and having a wall with at least two ducts (11, 12; 111, 112) passing therethrough and opening out radially into said cavity (10; 110); a piston (3; 103) housed in said cavity (10; 110) with which it co-operates to define a working chamber (31; 131) and including, in its cylindrical surface, a longitudinal channel (22; 122) or recess that opens out longitudinally into said working chamber (31; 131), said piston (3; 103) being provided with a sealing gasket (32, 33, 34) that is made of a material having a modulus of elasticity that is less than the moduli of elasticity of said piston and of said body, and that is carried by said piston (3; 103), the gasket running beside said channel so as to guarantee leaktight sealing between said piston (3; 103) and said cavity (10; 110), the piston being movable angularly so as to put said working chamber (31; 131) into fluid-flow communication with at least one, then none, then at least the other of said ducts (11, 12; 111, 112), and being movable in longitudinal translation to reciprocate so as to cause the volume of said working chamber (31; 131) to vary and successively suck in and then discharge said fluid via one then the other of said ducts (11, 12; 111, 112), said sub-assembly being characterized in that the piston (3; 103) includes a first axial end remote from a second axial end, said second axial end being in contact with the working chamber (31; 131); • said sealing gasket (32, 33, 34) is made up of a plurality of portions comprising: a first sealing portion in the shape of a ring that extends around the cylindrical surface of the piston (3; 103) beside its first axial end; a second sealing portion in the shape of a half-ring that extends around the cylindrical surface of the piston (3; 103) beside its second axial end, the half-ring having two ends that are spaced apart from each other over the cylindrical periphery of the piston; and a third sealing portion that is formed by two sealing strips that extend axially over the outside surface of the piston (3; 103) respectively between a first end of the half-ring and the ring, and between a second end of the half-ring and the ring; in that the two strips are angularly offset from each other and each defines: • a first sealing line that angularly borders said channel (22; 122), said first sealing lines being spaced apart from each other by an angle (α1) containing said channel (22; 122), that is greater than each of the angles (pi) between the edges of either one of the ducts (11, 12; 111, 112), and that is less than each of the angles between the adjacent edges of either one of the ducts (11; 111) and of its corresponding duct (12; 112); • and a second sealing line, each second sealing line being spaced apart from one of said first sealing lines by an angle (α2) that does not contain said channel (22; 122), that is less than each angle (β2) between the edge of one duct (11; 111) and the adjacent edge of its corresponding duct (12; 112), and that is greater than each angle (β1) between the opposite edges of either one of the ducts (11, 12; 111, 112); and in that • the angle (α3) between each first sealing line from at least one of the second sealing lines, and containing said channel (22; 122), is greater than the angle (β3) between the axially-opposite edges of the two ducts (11, 12; 111, 112). • said sealing gasket (32, 33, 34) is made up of a plurality of portions comprising: a first sealing portion in the shape of a ring that extends around the cylindrical surface of the piston (3; 103) beside its first axial end; a second sealing portion in the shape of a half-ring that extends around the cylindrical surface of the piston (3; 103) beside its second axial end, the half-ring having two ends that are spaced apart from each other over the cylindrical periphery of the piston; and a third sealing portion that is formed by two sealing strips that extend axially over the outside surface of the piston (3; 103) respectively between a first end of the half-ring and the ring, and between a second end of the half-ring and the ring; • a first sealing line that angularly borders said channel (22; 122), said first sealing lines being spaced apart from each other by an angle (α1) containing said channel (22; 122), that is greater than each of the angles (pi) between the edges of either one of the ducts (11, 12; 111, 112), and that is less than each of the angles between the adjacent edges of either one of the ducts (11; 111) and of its corresponding duct (12; 112); • and a second sealing line, each second sealing line being spaced apart from one of said first sealing lines by an angle (α2) that does not contain said channel (22; 122), that is less than each angle (β2) between the edge of one duct (11; 111) and the adjacent edge of its corresponding duct (12; 112), and that is greater than each angle (β1) between the opposite edges of either one of the ducts (11, 12; 111, 112); and in that • the angle (α3) between each first sealing line from at least one of the second sealing lines, and containing said channel (22; 122), is greater than the angle (β3) between the axially-opposite edges of the two ducts (11, 12; 111, 112).