We performed a combined density functional theory (DFT) and X-ray photoelectron spectroscopy (XPS) study of noncovalently bonded hybrids of 3d metal phthalocyanines MePcs (where M = Co, Ni, Cu and Zn) and single-walled carbon nanotubes (SWNT). The results of both DFT calculations (PBE functional in conjunction with the dispersion correction by Grimme and DNP basis set) and comparative XPS spectral measurements for neat MePcs and MePc + SWNT hybrids suggest very strong interactions between macrocyclic complexes and carbon nanotube sidewalls. DFT calculations produced very high absolute values of binding energies of 32.74-45.35 kcal/mol (depending on MePc and nanotube model). The macrocycles (planar in neat MePcs) suffer strong bending distortion in order to increase the area of their contact with nanotube sidewall. In many cases, N ... C-SWNT (and not Me ... C-SWNT) distances turn to be the closest approaches between MePc and SWNT model, where the nitrogen atoms forming them can be either one of the N atoms belonging to MeN4 coordination sphere, or one of the gamma-N atoms, with some of C-MePc ... C-SWNT closest approaches comparable in length with the shortest N ... C-SWNT distances. The calculated HOMO-LUMO gap energies are very low, from 0.007 to 0.622 eV only. The pattern of HOMO-LUMO distribution found in most cases is different from the one typically observed for noncovalent dyads of Pcs and porphyrins with carbon nanoclusters (fullerenes and carbon nanotubes), where HOMO is localized on the macrocyclic component and LUMO, on carbon nanocluster. The experimental XPS measurements found the existence of only one N 1s component for noncovalent MePc + SWNT complexes versus three components for neat phthalocyanine beta-polymorphs, as well as the decrease of multiplet splitting and the increase of spectral resolution observed for both N 1s and Me 2p peaks as a result of phthalocyanine deposition onto SWNTs.