over a first drive pulley of a first drive 7 1 for the first elevator car and a second drive pulley of a second drive 7 2 for the second elevator car a first or second electric motor of the first or second drive 7 1 or 7 2 can apply a torque to the first or second drive pulley so as to raise hold or lower the first or second elevator car 1 or 2 the elevator cars 1 2 arranged adjacent to one another in an elevator shaft 9 can thereby move independently of one another the support means 4 runs between the two drives 7 1 7 2 in opposite sense around a deflecting roller 5 4 at which a counterweight 3 is suspended so that the first and second elevator cars 1 2 are suspended in a 1 1 ratio and the counterweight 3 in a 2 1 ratio at the support means 4 i e the support means lowers in the ratio 1 2 when the first or second elevator car 1 or 2 is raised and vice versa a compensation means in the form of a belt 5 is attached to the underside of the first and second elevator cars 1 2 the compensation means runs starting from the first elevator car 1 around a first deflecting roller 5 1 mounted inertially in the shaft pit of the elevator shaft 9 subsequently loops in opposite sense around a third deflecting roller 5 3 fastened to the underside of the counterweight 3 runs from there again in opposite sense around a second deflecting roller 5 2 at which a compensating means tensioning device in the form of a tensioning weight 8 is suspended and is fastened at its other end to.