the invention relates to an elevator system in tall buildings , the system having at least one first elevator shaft , which houses an elevator arranged to stop at floors called transfer levels , and at least one second elevator shaft , which houses elevators whose elevator cars are disposed one above the other in the elevator shaft , which elevator cars are designed to stop during their travel at any floor to which or from which a call has been issued . the second elevator shaft is divided vertically into local shafts situated one above the other , the number of which is at least one for each zone between transfer levels .