The structure characteristics, interaction energies, cooperative energies of the complexes between chalcogen hydrides ( H2Y ) and halogen hydrides (HX) have been studied theoretically at the MP2 level with aug-cc-pVTZ basis set in this paper. The conclusions show that there are strong interactions between H2Y and HX. The stability of the complex is decided by the electronegativity of the negatively charged atom. The cooperativity is observed in the two or three hydrogen bonds of each trimer structures in title system. The values of the cooperative energies and the cooperative contributions all illustrate that the cooperativity is of great importance in these complexes. The "atoms in molecules" (AIM) analyses show that the complexes in title system are mainly electrostatic interactions (closed-shell interactions) in character. For H ⋯ O bonds in H2O ⋯ HF ⋯ H2O , H2O ⋯ HBr ⋯ H2O and HF ⋯ H2O ⋯ HF , the 1 < |Vc|/Gc< 2 and -Gc< Hc< 0 indicate the interactions in these compounds are between closed-shell interaction and opened-shell interaction.