Sliding door or window assembly, comprising - a frame part mounted to a building, the frame part having frame legs (2, 3, 4, 5) that are horizontal and situated at the bottom and the top, respectively, as well as two vertical, lateral frame legs, - at least one door or window wing (6.1 to 6.4) displaceable in the frame part between an open and a closed position, the wing (6.1 to 6.4) in each case having a pane element with a frame profile encompassing the edges of the pane elements, and - a pivotable sealing lip assembly (11.1, 11.2) along at least one of the frame legs, said sealing lip assembly = being pivotally mounted in the frame leg about a pivot axis extending parallel to the longitudinal direction of the frame leg, and = being movable from a retracted inactive position into a sealing position abutting against the adjacent frame profile of the wing (6.1) at least in the closed position of the wing (6.1 to 6.4), characterized in that - a drive kinematics system (24, 24') is provided for the at least one sealing lip assembly (11.1, 11.2), said drive kinematics system (24, 24') being driven by means of an actuation handle, preferably a locking turning handle of the sliding door or window assembly, and - the drive kinematics system (24, 24') having a crank assembly (28u, 28o) comprising a connecting rod element and a crank element, the crank assembly (28u, 28o) converting a linear driving movement of a driving slider, said movement being derived from the actuation handle, into the pivoting movement of the at least one sealing lip assembly (11.1, 11.2). - a frame part mounted to a building, the frame part having frame legs (2, 3, 4, 5) that are horizontal and situated at the bottom and the top, respectively, as well as two vertical, lateral frame legs, - at least one door or window wing (6.1 to 6.4) displaceable in the frame part between an open and a closed position, the wing (6.1 to 6.4) in each case having a pane element with a frame profile encompassing the edges of the pane elements, and - a pivotable sealing lip assembly (11.1, 11.2) along at least one of the frame legs, said sealing lip assembly = being pivotally mounted in the frame leg about a pivot axis extending parallel to the longitudinal direction of the frame leg, and = being movable from a retracted inactive position into a sealing position abutting against the adjacent frame profile of the wing (6.1) at least in the closed position of the wing (6.1 to 6.4), = being pivotally mounted in the frame leg about a pivot axis extending parallel to the longitudinal direction of the frame leg, and = being movable from a retracted inactive position into a sealing position abutting against the adjacent frame profile of the wing (6.1) at least in the closed position of the wing (6.1 to 6.4), - a drive kinematics system (24, 24') is provided for the at least one sealing lip assembly (11.1, 11.2), said drive kinematics system (24, 24') being driven by means of an actuation handle, preferably a locking turning handle of the sliding door or window assembly, and - the drive kinematics system (24, 24') having a crank assembly (28u, 28o) comprising a connecting rod element and a crank element, the crank assembly (28u, 28o) converting a linear driving movement of a driving slider, said movement being derived from the actuation handle, into the pivoting movement of the at least one sealing lip assembly (11.1, 11.2).