The interactions of Cu(S-2:3d(10)4s(1), D-2:3d(9)4s(2), and P-2:3d(10)4p(1)) with SiH4 and GeH4 were studied by means of Hartree-Fock-SCF and multiconfigurational-SCF followed by variational and multireference second order Moller-Plesset perturbational configuration interaction (CIPSI) calculations, using relativistic effective core potentials. The Cu atom in its P-2(3d(10)4p(1)) state is inserted in the Si-H and Ge-H bonds. In both interactions their corresponding 5 (2)A(') potential energy surfaces are initially attractive and become repulsive only after having encountered the avoided crossing region with the initially repulsive 4 (2)A(') surface adiabatically linked with the Cu(D-2:3d(9)4s(2))-SiH4(GeH4) fragments. The three (2)A(') curves derived from the interaction of the Cu(D-2:3d(9)4s(2)) atom with silicon (or germane) molecule are initially repulsive. Each one of them shows two avoided crossings and its lowest lying 2 (2)A(') curve goes sharply down until it meets the X (2)A(') curve adiabatically linked with the Cu(S-2:3d(10)4s(1))+SiH4(GeH4) asymptotes. The 2 (2)A(') curve becomes repulsive after the avoided crossing with the X (2)A(') curve. The lowest-lying X (2)A(') potential leads to the HCuZH(3) X (2)A(1) (Z=Si, Ge) intermediate molecule. This intermediate molecule, diabatically correlated with the Cu(P-2:3d(10)4p(1))+ZH(4) fragments which lie 5.8 and 1.6 kcal/mol, respectively, above the ground state reactants, have been carefully characterized as well as the dissociation channels leading to the CuH+ZH(3) and H+CuZH(3) products. These products are reached from the HCuZH(3) intermediates without activation barriers. This work suggests that the simultaneous photoexcitation of the Cu atom in presence of silane and germane molecules in the gas phase could be used to produce better quality a-SiGe:H thin films.