pi-proton-donor and :T-acceptor systems were investigated by ab initio quantum-chemical calculations. C2H2...H+...C2H2 and C2H4...H+...C2H2 complexes were optimized using the MP2 level of theory; 6-311++G(d,p), 6-311++G(2d,2p), 6-311++G(3d,3p), and aug-cc-pVDZ basis sets were applied. Their geometrical and energetic characteristics were compared with characteristics of the other systems with conventional and unconventional H bonds. Such a comparison indicates that pi...H+...pi complexes may be classified as hydrogen bonded. The binding energies for C2H2...H+...C2H2 and C2H4...H+...C2H2 calculated at the MP2/aug-cc-pVDZ level are equal to 15.0 and 10.4 kcal/mol, respectively (basis set superposition error included), which correspond to medium or strong H bonds. The Bader theory was applied to characterize the bond-critical points (BCPs) of H+...pi contacts. The electron densities at H+...T BCPs also indicate that such systems possess hydrogen bonds of medium strength. To obtain better insight into the nature of these interactions, the variation-perturbation approach was applied to evaluate components of the interaction energy.