An elevator drive has a driving engine, a brake (6) and a two-stage planetary gear (9). Both stages (8, 10) of the planetary gear have helical toothing. The sun wheel (15) of the second planetary gear stage (10) is floatingly mounted in a hub-carrier (17) or hub (21, 23) on a bearing (16) that absorbs axial and radial forces. This arrangement reduces the axial overall length. The sun wheels (7, 15) of the planetary gear stages (8, 10) may adapt to load conditions. The helical toothing of the planetary (9) prevents low-frequency vibrations which may propagate up to the lift cabin, specially when they are transmitted over long cables, and could be perceived there as a disturbing humming noise.