An elevator includes first and second elevator units vertically movable in a hoistway and interconnected by at least one belt-shaped hoisting rope. Each of the belt-shaped hoisting ropes is moved and passes around a drive wheel and includes consecutively a first rope section extending between the drive wheel and the first elevator unit, and a second rope section extending between the drive wheel and the second elevator unit. The elevator further includes non-driven cambered diverting wheels, each said first and second rope section being arranged to pass around and rest against a cambered circumferential surface area thereof. A monitoring arrangement monitors displacement of the first and second rope sections of the wheels in the axial direction. When one or more of the first and second rope sections is displaced in the axial direction of the wheels away from a predefined zone, rotation of the drive wheel is stopped.