B3LYP level density functional theory(DFT) and multiconfiguration self-consistent-field (MCSCF) level ab initio method calculations have been performed on the basis of relativistic effective core potentials to investigate the nature of EuC and EuC2 molecules. The computed results indicate that the ground states of EuC and EuC2 are 12 Σ+ and 8A2, respectively. Dissociation potential energy curves of the low-lying electronic states of EuC have been calculated using the MCSCF method, and the same level calculation on EuC2 indicates that the dissociation energy of EuC2of ground state compares well with the available experimental data. The bond characteristic is also discussed using Mulliken populations.