Each of a pair of vertically and horizontally adjacent hoistways has an elevator car coupler roped through a traction machine to a counterweight so as to be able to raise and lower the elevator car within the related hoistway. A transition section joins the upper end of the lower hoistway with the lower end of the upper hoistway. A pair of guide rails are disposed on each side of the elevator system, including the upper hoistway, the transition section and the lower hoistway. Elevator cars are guided from the top of the upper hoistway to the bottom of the lower hoistway and/or vice versa by one of the pairs of rails. Power in the transition section is provided by a pair of LEMs, one on each side of the hoistways.