Interactions between carbohydrates and aromatic amino-acid residues are often observed in structures of carbohydrate-protein complexes. They are characterized by an orientation of the pyranose or furanose ring parallel with the aromatic ring of amino-acid residues. An important role in the formation of these complexes is supposed to be played by CH/pi interactions. This paper presents an ab initio quantum chemistry study of CH/pi interactions between beta-galactosidase from E. coli and its substrates and products. The energy stabilizing the interaction between Trp999 residue and substrate bound in the shallow binding mode was calculated at the MP2/6-31+G(d) level as 5.2kcalmol(-1) for the glucose moiety of allolactose, 2.4kcalmol(-1) for the galactose moiety of allolactose and 5.0kcalmol(-1) for the glucose moiety of lactose. The energy stabilizing the interaction between Trp568 residue and galactose in the deep binding mode was calculated as 2.7kcalmol(-1). Interaction energies at the HF/6-31+G(d) and B3LYP/6-31+G(d) levels were small or repulsive; therefore, highly correlated ab initio methods were necessary to study these interactions. These unexpectedly strong interactions give a rationale for allolactose formation and illustrate the role of the Trp999 residue. In addition, this illustrates the importance of CH/pi interactions for the function of carbohydrate-binding proteins and carbohydrate-processing enzymes.