In this paper we analyze the formation of stripes of expression of the pair-rule gene eve. We identify detailed mechanisms which control the formation of stripes 2-5. Each stripe is formed as a result of generalized activation by bcd and ubiquitous transcription factors combined with localized repression by gap genes. Each of the eight stripe borders of these four stripes is shown to be under the control of a particular gap gene expression domain. Protein synthesis from eve and its controlling gap genes begins at the same time, but localized eve expression is substantially delayed relative to localized expression of gap domains. We show that this delay results from a change in the spatial balance between activation and repression due to the intensification and refinement of gap domains during cleavage cycle 14. eve stripe formation is ordered in time; stripe 2 appears earlier than stripes 3-5. We show that this happens because the formation of stripe 2 is less dependent on gap domain refinement than is the case for stripes 3-5: Each of stripes 3-5 is controlled by a pair of overlapping gap domains, whereas stripe 2 is controlled by a disjoint pair of gap domains. Finally, we observe that eve stripes do not form unless Eve protein has an extremely small diffusivity, and argue that this low diffusivity is a result of the apical localization of pair-rule message. This implies that localization of pair-rule message is required for stripe formation. The essential tool used to obtain these results is the method of gene circuits, which is a new approach to the analysis of gene expression data. Its purpose is to provide a way to use this data to infer how concentrations of products of a given gene change with time and how these changes are influenced by the activating or repressing effects of the products of other genes. The gene circuit method is based on three main ideas, explained in the paper. First is the choice of protein concentrations as state variables for the description of gene regulation. Second is the summary of chemical reaction kinetics by coarse-grained rate equations for protein concentrations. Third is the use of least squares fits to gene expression data to measure phenomenological parameters occurring in the gene circuit.