The pair-rule genes hairy, runt, even-skipped, and fushi tarazu express their mRNAs and proteins in striped patterns in the Drosophila embryo at the blastoderm stage. Previous studies have shown that the generation of these patterns depends upon products of the gap genes and upon interactions between the pair-rule genes themselves. Here we show that blocking protein synthesis induces expression of each of the pair-rule mRNAs in virtually all regions of the embryo. Our observations together with genetic studies carried out in other laboratories suggest that negative feedback between the pair-rule genes plays a key role in striped expression of pair-rule genes. We propose that stable proteins, present in all regions of the embryo, first activate transcription of these pair-rule genes constitutively. Then, various combinations of unstable proteins repress their transcription in a patterned fashion; each stripe of accumulated products of a given pair-rule gene marks a region where it was not repressed. We develop this idea in mathematical form and demonstrate that a network of mutual repression by pair-rule genes can make each blastoderm nucleus into a genetic switch with two stable states. If preexisting gap gene patterns provide initial bias to the blastoderm nuclei, then the "bistable switch behavior" of the nuclei can refine an initially weak spatial bias into a final pattern of sharp stripes.