The invention relates to a double-seat valve, the seats of which can be cleaned and which is improved with respect to the prior art in such a way that the seat-cleaning flow can be directed into and out of the hollow leakage space with as few eddies as possible while the seat areas are securely protected against direct increasing pressurization. In order to do so, among other things, the double-seat valve (1) is fitted with closing members (3, 4) which can be independently moved into a seat-cleaning position by being partly lifted to form a gap in order to rinse the coaxial seat surfaces (2a, 2b) thereof. The second closing member (4) is brought into the seat-cleaning position thereof by means of a second partial lift (T2) in the same direction as the opening movement, while the first closing member (3) is brought into the seat-cleaning position thereof by means of a first partial lift (T1) in the direction opposite the opening direction. Furthermore, in the closed position, a stop surface (4T) of the second closing member (4) rests on the second seat surface (2b), immediately adjacent to first seat surface (2a), said stop surface (4T) forming a second circumferential edge (U2) along with the peripheral wall (4c; 4h). In addition, the peripheral wall (4c) turns into a rotationally symmetrical deflection surface (4d) (starting point of a contour (K)) at the end thereof facing away from the first closing member (3), and said deflection surface (4d) extends into a face (4e) of the cavity (4b) (final point of the contour (K)), said face (4e) of the cavity (4b) running substantially perpendicular to the longitudinal axis of the second closing member (4). Moreover, the contour (K) of the deflection surface (4d) has no sharp bends from a meridian cross-sectional view. And finally, a directional vector in the final point of the deflection surface (4d) points to a concentric discharge bore (3d; 3d*) located in the first closing member (3) without colliding with the closing member (3) and generating banking-up pressure in the area of the zones thereof which border the hollow leakage space (5).