If regulation is to play a significant part in the evolution of molecular functions, understanding the evolvability of its genomic encoding is an important challenge. Cis-regulatory elements in eukaryotes are often organized in modules of several adjacent sites binding to combinations of transcription factors. Estimates of binding site evolution under selection show that point substitutions alone are not a sufficiently fast mode to produce such modules, and the dominant modes of their evolution have remained unclear. In this work, we investigate local sequence duplications as a possible mode for module formation. Genomic analysis shows a significant autocorrelation in Drosophila regulatory modules: sequence segments of about 10 bp length are correlated up to a relative distance of several tens of base pairs. We link this correlation with similarity of functional units which we explain in terms of an evolutionary model for binding site formation in the modules. We find that adjacent functional sites, for different factors in general, are more likely to share a common ancestor sequence than to have evolved from independent ancestors. Our results suggest that local sequence duplication is an important mode in evolution of regulatory modules.