A quick coupling (R) for the detachable connection of two pipes (C1, C2) through which a pressurized fluid flows, made up of a male element and a female element able to receive the male element by fitting along a longitudinal axis (X-X') between an uncoupled configuration and a coupled configuration, the male element comprising: - a cylindrical male body , defining a longitudinal cavity and a distal mouth , the diameter (D106) of which is smaller than that (D104) of the cavity, - a valve movable axially inside the cavity, between a forward position in which the valve closes off the mouth and a withdrawn position in which the valve does not close off the mouth, and - a first sealing gasket , which is borne by the valve or the male body, and which bears respectively on an inner cylindrical wall (S102i) of the male body or on an outer cylindrical wall of the valve (S108e), when the valve is in the forward position, and the female coupling element comprising: - a cylindrical female body , defining a longitudinal cavity and a distal mouth , the diameter (D206) of which is smaller than or equal to that (D204) of the cavity, - a slide valve , which is movable axially inside the longitudinal cavity between a forward position, in which the slide valve closes off the mouth , and a withdrawn position, in which the slide valve does not close off the mouth, and - a second sealing gasket , which is borne by a member from among a central push-piece secured to the female body, the slide valve or the female body and which bears on another member from among the slide valve, the push-piece or the female body, when the slide valve is in the forward position, wherein the first or the second sealing gasket is housed inside a peripheral groove (111; 211), characterized in that a proximal (111b; 211b) or distal (111a; 211a) edge of the peripheral groove extends between two planes that are perpendicular to a longitudinal axis (X100; X200) of the male or female element, respectively between a proximal plane (P1) and a distal plane (P2), which are offset relative to one another along the longitudinal axis. - a cylindrical male body , defining a longitudinal cavity and a distal mouth , the diameter (D106) of which is smaller than that (D104) of the cavity, - a valve movable axially inside the cavity, between a forward position in which the valve closes off the mouth and a withdrawn position in which the valve does not close off the mouth, and - a first sealing gasket , which is borne by the valve or the male body, and which bears respectively on an inner cylindrical wall (S102i) of the male body or on an outer cylindrical wall of the valve (S108e), when the valve is in the forward position, - a cylindrical female body , defining a longitudinal cavity and a distal mouth , the diameter (D206) of which is smaller than or equal to that (D204) of the cavity, - a slide valve , which is movable axially inside the longitudinal cavity between a forward position, in which the slide valve closes off the mouth , and a withdrawn position, in which the slide valve does not close off the mouth, and - a second sealing gasket , which is borne by a member from among a central push-piece secured to the female body, the slide valve or the female body and which bears on another member from among the slide valve, the push-piece or the female body, when the slide valve is in the forward position, <EOS>