Due to high cost, considerable complexity and long design cycles of fault-tolerant systems, a (partial) automation of the design process becomes attractive. This paper presents an approach to automatic design by use of a genetic algorithm. Unlike typical genetic algorithms the individuals (which represent a fault-tolerant system structure each) are represented by a non-cyclic graph rather than a string. Special crossover and mutation operations modify the individuals such that reasonable fault-tolerant systems are likely to be generated. The biggest problem in using genetic algorithms lies in the definition of an appropriate fitness function one has to apply to each of the many generated individuals. A complete analysis of a single fault-tolerant system would comprise time-consuming fault-tree analysis, reachability analysis of the state space, etc. A substantial speed-up by orders of magnitude has been achieved by the development of a completely new fitness function, which can be considered as a simplified reachability analysis. For many fault tolerance techniques it visits each component only once (or very few times in the case of mechanisms like rollback, retry etc.).