A stroller accessory, which is connectable to a stroller so as together to form a double stroller and that is unusable to transport a child when the accessory is disconnected from the stroller, wherein the accessory includes: - a frame that, during use, bears a receiving member in which a child to be transported can be installed, - a connection mechanism for reversibly connecting the accessory to the stroller in order to form the double stroller, this connection mechanism being borne by a front part of the frame of the accessory and being suitable for securing this front part of the frame of the accessory removably to a rear part of a frame of the stroller so as both to arrange the accessory behind the stroller in a front-back direction and to define a tilting axis, which extends during use substantially parallel to the ground and substantially perpendicular to the front-back direction and around which the front part of the frame of the accessory and the rear part of the frame of the stroller tilt freely relative to one another, - two wheels (230G, 230D), which, when the accessory is connected to the stroller by the connection mechanism, bear and roll on the ground and which are coupled to a rear part of the frame of the accessory so as to pivot around respective pivot axes (Z230G, Z230D), - a pushing member, which is borne by the rear part of the frame of the accessory and which is suitable for being urged manually by a user standing behind the double stroller, - a control mechanism for controlling a rolling blocking of the double stroller, this control mechanism being borne by the front part of the frame of the accessory and being suitable, when the accessory is connected to the stroller by the connection mechanism, for cooperating mechanically with a rolling blocking system, integrated into the stroller, so as to control this rolling blocking system, and - an actuating member that is borne by the rear part of the frame of the accessory so as to be able to be activated by a user standing behind the double stroller, and that is coupled to the control mechanism so as to actuate this control mechanism. - a frame that, during use, bears a receiving member in which a child to be transported can be installed, - a connection mechanism for reversibly connecting the accessory to the stroller in order to form the double stroller, this connection mechanism being borne by a front part of the frame of the accessory and being suitable for securing this front part of the frame of the accessory removably to a rear part of a frame of the stroller so as both to arrange the accessory behind the stroller in a front-back direction and to define a tilting axis, which extends during use substantially parallel to the ground and substantially perpendicular to the front-back direction and around which the front part of the frame of the accessory and the rear part of the frame of the stroller tilt freely relative to one another, - two wheels (230G, 230D), which, when the accessory is connected to the stroller by the connection mechanism, bear and roll on the ground and which are coupled to a rear part of the frame of the accessory so as to pivot around respective pivot axes (Z230G, Z230D), - a pushing member, which is borne by the rear part of the frame of the accessory and which is suitable for being urged manually by a user standing behind the double stroller, - a control mechanism for controlling a rolling blocking of the double stroller, this control mechanism being borne by the front part of the frame of the accessory and being suitable, when the accessory is connected to the stroller by the connection mechanism, for cooperating mechanically with a rolling blocking system, integrated into the stroller, so as to control this rolling blocking system, and - an actuating member that is borne by the rear part of the frame of the accessory so as to be able to be activated by a user standing behind the double stroller, and that is coupled to the control mechanism so as to actuate this control mechanism.