The invention relates to an elevator system (10) for a building under construction, comprising a vertical shaft (12), in which a temporary machine compartment (14) is retained, a driving device (18), which is arranged in the temporary machine compartment (14) and which is coupled by means of a supporting cable (21) to a car (23) that can be moved vertically up and down in the shaft (12), and a speed limiter (30), which interacts with a speed limiter cable (34) arranged in the shaft (12). According to the invention, in order to develop the elevator system in such a way that the speed limiter cable (34) can be extended in a simple manner when the temporary machine compartment (14) is moved without said action leading to permanently increased energy consumption of the elevator system (10), the speed limiter (30) is arranged on the car (23) or on a counterweight (25) connected to the car (23) by means of the supporting cable (21), and that the speed limiter cable (34) has a first and second cable section (32, 52), wherein the first cable section (32) is clamped in a stationary manner between a cable retainer (46) connected to the temporary machine compartment (14) in a stationary manner and a releasable clamping device (50) arranged in a lower shaft region (48) and the second cable section (52) is connected to the first cable section (32) in the lower shaft region (48) and is stored in a storage region.