The properties of six dihydrogen-bonded (DHB) dimers with the BeH2 molecule as a proton acceptor were calculated by MP2, CCSD(T) and B3LYP methods. The structural, energetic and spectroscopic parameters are presented and analyzed in terms of their possible correlation with the interaction energy and the intermolecular H...H separation. The symmetry-adapted perturbation theory (SAPT) calculations were performed to gain more insight into the nature of the H...H interactions. The studied complexes are divided into three groups based on the calculated intermolecular distances and the interaction energies which range from approximately -1 to -42 kJ mol(-1). The analysis of the interaction energy components indicates that, in contrast to conventional hydrogen bonds, the induction energy is the most important term in the BeH2NH4+ complex. On the other hand, there is no sharp boundary between the DHB complexes classified as hydrogen bonded and van der Waals systems. The complexation-induced changes in vibrational frequencies and in proton shielding constants show a relationship with the interaction energy. The values of the 2hJXH and 3hJBeX coupling constants correlate well with the interaction energy and with the intermolecular distance.