Sliding door assembly comprising a running rail which defines a longitudinal axis and has a side web and an upper web, a door leaf which is displaceable parallel to a plane formed by the longitudinal axis and a vertical axis perpendicular to the longitudinal axis, wherein the door leaf is suspended from two carriages guided in the running rail, a damper connected to the door leaf, which is arranged between the two carriages and has a driver, and an activator which has a coupling element which co-operates with the driver and which is disengaged from the driver in a disengaged position and engaged with the driver in an engaged position, wherein the activator has a retaining portion which is received in a guide recess formed on an underside of the upper web, wherein the guide recess is delimited on a side facing the carriage by an inner guide portion and an outer guide portion, wherein a longitudinal slot with a width (d 31) is formed between the two guide portions (29, 30), and wherein the retaining portion has projections (32, 33) which are arranged in the guide recess and engage behind the guide portions, characterised in that the activator is designed to be rotatable about the vertical axis by a limited angular range into a blocking position, in which a transverse extension of the retaining portion orientated perpendicular to the longitudinal axis is greater than the width (d 31) of the longitudinal slot and less than or equal to a clear width (d 39) of the guide recess, and into a release position, in which a transverse extension of the retaining portion aligned perpendicular to the longitudinal axis is less than or equal to the width (d 31) of the longitudinal slot, wherein the projections (32, 33) engage behind the guide portions in the blocking position. a running rail which defines a longitudinal axis and has a side web and an upper web, a door leaf which is displaceable parallel to a plane formed by the longitudinal axis and a vertical axis perpendicular to the longitudinal axis, wherein the door leaf is suspended from two carriages guided in the running rail, a damper connected to the door leaf, which is arranged between the two carriages and has a driver, and an activator which has a coupling element which co-operates with the driver and which is disengaged from the driver in a disengaged position and engaged with the driver in an engaged position, wherein the activator has a retaining portion which is received in a guide recess formed on an underside of the upper web, wherein the guide recess is delimited on a side facing the carriage by an inner guide portion and an outer guide portion, wherein a longitudinal slot with a width (d 31) is formed between the two guide portions (29, 30), and wherein the retaining portion has projections (32, 33) which are arranged in the guide recess and engage behind the guide portions, characterised in that the activator is designed to be rotatable about the vertical axis by a limited angular range into a blocking position, in which a transverse extension of the retaining portion orientated perpendicular to the longitudinal axis is greater than the width (d 31) of the longitudinal slot and less than or equal to a clear width (d 39) of the guide recess, and into a release position, in which a transverse extension of the retaining portion aligned perpendicular to the longitudinal axis is less than or equal to the width (d 31) of the longitudinal slot, wherein the projections (32, 33) engage behind the guide portions in the blocking position.