The Bicoid (Bcd) protein is a concentration-dependent transcriptional activator in the embryo of Drosophila melanogaster. Bcd regulates the expression of the maternal and zygotic gene hunchback (hb) that shows a step-like-function expression pattern, in the anterior half of the egg. The regulatory region of hb contains six major binding sites for the Bcd protein, named A1, A2, A3 (strong sites), and X1, X2, X3 (weak sites). Cooperativity between Bcd molecules binding to the hb enhancer element has been characterized as an important mechanism for the step-like shape of hb anterior expression domain. The objective of the present report is to analyse the mechanism of this cooperative binding based on a reaction network model. Using this method we have analysed experimental results from the literature describing how the Bcd protein binds to hb enhancer elements containing the A1 or X1 site alone or these two sites together at wild type distance. This approach allows us to estimate the kinetic constants of protein-protein and protein-DNA interactions. Moreover our results suggest that binding of a Bcd dimer to the hb enhancer element is more stable than binding of a monomer. We propose a cooperative kinetic mechanism for binding of Bcd to the hb enhancer element: First, a monomer binds to the site with a relatively low affinity; after that, another monomer binds to the first one with higher affinity, generating a dimer bound to the site. This yet unreported monomer-monomer cooperative mechanism takes place for occupancy of either one-site or two-site enhancer elements. In addition, we find cooperativity between neighbor sites, as previously reported in the literature.