The gas-phase interaction of H3CCH2XH3 and H2CC(H)XH3 (X=C, Si, Ge) with Cu+ has been investigated through the use of high-level density functional theory methods. The structures of the corresponding Cu+-complexes were optimized at the B3LYP/6-311G(d,p) level of theory, while the final energies were obtained in single-point B3LYP/6-311+G(2df,2p) calculations. In all cases, the most stable complexes are stabilized through agostic interactions between the metal cation and the hydrogen atoms of the XH3 group. Only for the unsaturated derivatives, the interaction with the CC double bond competes with these agostic interactions, although the π-complexes for Si and Ge derivatives are slightly less stable. Since these interactions increase with the hydride character of the hydrogen atoms involved, ethylsilane and ethylgermane are predicted to bind Cu+ much more strongly than propane. Conversely, vinylsilane and vinylgermane are predicted to have slightly lower Cu+ binding energies than propene. These agostic interactions lead to a significant weakening of the XH linkages involved, reflected in a very large red shifting of the XH stretching frequency. A topological analysis of the charge density of these complexes seems to be a powerful tool to detect and characterize these agostic bonds. Actually, we have found a good correlation between the charge density at the agostic bond critical point and the stability of the complex.