The invention relates to an elevator installation, comprising a shaft, in which a first car (22) and a second car (24) arranged below the first car can be moved up and down in a vertical direction along a common track separately from each other. The first car is coupled to a first counterweight (28) by means of first support cables (26) or support belts and by means of first under cables (62; 122) or under belts and the second car is coupled to a second counterweight (42) by means of second support cables (40) or support belts and second under cables or under belts. In order to further develop the elevator installation in such a way that the elevator installation has simpler cable or belt guidance for the first under cables or under belts, the first under cables or under belts according to the invention have a first and a second cable end or belt end (64, 90, 124, 126), wherein the first under cables or under belts are fastened either to the first counterweight or to the first car by means of the two cable ends or belt ends and are guided around at least one roller (82, 128, 130) arranged on the underside of the first car or on the first counterweight.