The cationic (C2H4)M(+) complexes (M = Cu, Ag, and Au) have been examined by different ab initio molecular orbital, density functional (DFT), and density functional/Hartree-Fock (DFT/HF) hybrid methods using relativistic effective core potentials acid a quasi-relativistic approach to account for relativistic effects. For (C2H4Au+ a substantial relativistic stabilization is observed, such that the computed binding energies are almost twice as high than for (C2H4Ag+ and still significantly higher than for (C2H4Cu+. Structural features and energetics obtained at the various computational levels, although they differ significantly in their computational demands, are in satisfying agreement with each other, adding to the level of confidence that can be attributed to the computationally economic DFT and DFT/HF hybrid methods. In order to determine the nature of the bonding in these (C2H4)M(+) complexes, an energy decomposition scheme is applied to the DFT results. For all three metal cations, the interaction with ethylene shows large covalent contributions. The major part of the covalent terms stems from sigma-donor contribution from the ligand to the metal, whereas pi-acceptor bonding (back-bonding) is less important. An atoms-in-molecules (ATM) analysis of the charge density distribution reveals cyclic structures for (C2H4Au+ and (C2H4Cu+, whereas (C2H4Ag+ is T-shaped.