The second order Moller-Plesset (MP2) to the fourth order many-body perturbation theory including single, double, triple, and quadruple substitutions (MP4(SDTQ)), coupled cluster with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], quadratic configuration interaction with single and double substitutions (QCISD), and QCISD including noniterative triples contributions [QCISD(T)] ab initio correlated levels of theory have been employed in studies on molecular geometry and stability of the Ar-HCO+ and He-HCO+ complexes. Triple-zeta split-valence (6-311G) and correlation consistent (cc-pVTZ) basis sets augmented with diffuse and polarization functions were used. At applied levels of theory the predicted interaction energies (corrected for the basis set superposition error and zero-point vibrational energy) for Ar-HCO+ range from -3.21 kcal/mol (QCISD/6-311G(2df,2pd) to -4.21 kcal/mol (MP4(SDTQ)/aug-cc-pVTZ), and for He-HCO+ vary from -0.12 kcal/mol (-42 cm(-1), MP2/cc-pVTZ) to -0.37 kcal/mol (-130 cm(-1), CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ). The optimized Ar-H distance (2.1392 Angstrom at QCISD/cc-pVTZ and 2.1222 Angstrom at MP2/aug-cc-pVTZ) agrees very well with the experimentally determined (2.13 Angstrom) value, whereas when step-by-step higher level methods and basis sets are applied, the predicted He-H distance (1.9156 Angstrom at QCISD(T)/aug-cc-pVTZ dramatically retreats from the experimental value of 2.00 Angstrom.