An elevator installation includes a shaft in which a first elevator car and a second elevator car arranged below the first elevator car are movable upward and downward in the vertical direction separately from each other. Each elevator car is coupled to a counterweight via a rope or belt arrangement. At least one rope or belt arrangement has two rope or belt sections via which one of the elevator cars is coupled to a counterweight and which extend laterally along the other elevator car. In order to avoid impairment of an elevator car by rope or belt oscillations, the elevator car has at least one limiting member which is held in a predetermined position in the shaft and is assigned to a rope or belt section and has at least one limiting element which is movable between a limiting position and a release position depending on the position of the elevator car which is coupled to the counterweight via the associated rope or belt section. In the limiting position, the limiting element can be positioned on that side of the rope or belt section which faces the elevator car, and, in the release position, the limiting element releases said side.