This paper presents a theory of convergence for real-coded genetic algorithms—GAs that use floating-point or other high-cardinality codings in their chromosomes. The theory is consistent with the theory of schemata and postulates that selection dominates early GA performance and restricts subsequent search to intervals with above-average function value dimension by dimension. These intervals may be further subdivided on the basis of their attraction under genetic hillclimbing. Each of these subintervals is called a virtual character, and the collection of characters along a given dimension is called a virtual alphabet. It is the virtual alphabet that is searched during the recombinative phase of the genetic algorithm, and in many problems this is sufficient to ensure that good solutions are found. Although the theory helps explain why many problems have been solved using real-coded GAs, it also suggests that real-coded GAs can be blocked from further progress in those situations when local optima separate the virtual characters from the global optimum.