In order to reinforce a rear part of a convertible vehicle, reinforcement elements are provided on both sides on a rollover protection device. The reinforcement elements are composed, at the rear side of the device when viewed in the direction of travel, of at least two diagonal struts which extend toward one another. Further reinforcement elements are composed, at the front side of the device when viewed in the direction of travel, of at least two lateral stays which are arranged diverging from one another. The diagonal struts and the stays are secured supported on the vehicle body.