The mutual interaction between beryllium bonds and halogen bonds within H2Be center dot center dot center dot FCl center dot center dot center dot Base complexes, where Base includes a wide set of N- and O-containing Lewis bases, has been studied at the M06-2X/6-31+G(d,p) level of theory. The reliability of this theoretical model was assessed by comparison with ab initio CCSD/aug-cc-pVTZ reference calculations. Cooperative effects were investigated within the framework of the atoms in molecules theory (AIM) by analyzing the topology of the electron density and the changes in the atomic energy components. The decomposition of the total stabilization energy into atomic components is found to be a very reliable tool to describe halogen bond interactions. Both the topological analysis of the electron density and the changes in the atomic energy components of the binding energy show the existence of strong cooperative effects between beryllium and halogen bonds, which are in some cases very intense. In general, there is a correlation between the intrinsic basicity of the Lewis base participating in the halogen bond and the resulting cooperativity in the sense that the stronger the base, the larger the cooperative effects.