Genetic redundancy means that two or more genes are performing the same function and that inactivation of one of these genes has little or no effect on the biological phenotype. Redundancy seems to be widespread in genomes of higher organisms. Examples of apparently redundant genes come from numerous studies of developmental biology, immunology, neurobiology and the cell cycle. Yet there is a problem: genes encoding functional proteins must be under selection pressure. If a gene was truly redundant then it would not be protected against the accumulation of deleterious mutations. A widespread view is therefore that such redundancy cannot be evolutionarily stable. Here we develop a simple genetic model to analyse selection pressures acting on redundant genes. We present four cases that can explain why genetic redundancy is common. In three cases, redundancy is even evolutionarily stable. Our theory provides a framework for exploring the evolution of genetic organization.