We have determined the stable structures of AuCun, Au2Cun, Au3Cun and AuxCu8-x clusters. It has been observed that AuCun, Au2Cun and Au3Cun systems have two-dimensional (2D) structures up to six atoms and they become three-dimensional (3D) afterwards. AuxCu8-x clusters favor 3D structures till the Au7Cu1 cluster. We have found a lowest energy isomer of Au6Cu2 from the literature. Bond lengths, binding energies, density of states (DOS), highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps, ionization potential (IP) and electron affinity (EA) have been calculated for these structures using the first principles density functional theory (DFT) within the generalized gradient approximation (GGA) and the local density approximation (LDA). Generally, we have observed the overlap between s electrons of Cu and p electrons of Au near the Fermi level. Charge transfers are calculated by using the Lowdin analysis. It is observed that one Cu atom does not significantly modify the clusters which have more gold atoms. It is also seen that these clusters generally have nonmagnetic properties and results are consistent with the hybridization between s and d orbitals of Au in AuxCu8 (x) clusters.