An elevator system has a drive, a car, a plurality of safety function components for providing safety functions at various positions, and a safety monitoring system with a plurality of safety monitoring units for monitoring all of the safety function components. The monitoring units have an input interface for reading in data or signals and an output interface for outputting control signals to an assigned member of the safety function components, at least some of the monitoring units being connected via data exchange channels. The monitoring units are organized in a master-slave hierarchy, with one unit designed as a master unit, and at least one other unit designed as a slave unit. The decentralized and distributed monitoring units, each having data processing capability, and the master-slave organization result in the elevator system exhibiting a high security level with low cabling complexity and cost expenditure, in particular for high rise elevators.