The (3)Sigma(-) and (3)Pi states for the GeC and GeSi diatomics have been investigated at the highly correlated coupled-cluster levels of theory. Large basis sets [including TZ3P(2d,2f)+2diff, cc-pVQZ, and aug-cc-pVQZ] were employed in order to predict reliable values for the experimentally unknown spectroscopic properties. The ground states were confirmed to be the (3)Pi state for GeC and the (3)Sigma(-) state for GeSi. Advanced theoretical treatments such as inclusion of core-valence correlation, scalar relativity, and complete basis set extrapolations have been performed to determine accurate energetic properties. The dissociation energies (D-0) of 91.4 kcal/mol and 72.9 kcal/mol have been predicted for the X (3)Pi state of GeC and X (3)Sigma(-) state of GeSi, respectively. It is observed that the theoretical value of 72.9 kcal/mol for GeSi is in very good agreement with the experimental value of 71+/-5 kcal/mol. However, the predicted dissociation energy for the X (3)Pi state of GeC is found to be 18 kcal/mol smaller than the mass spectrometric measurements. Both the X (3)Pi and A (3)Sigma(-) state potential energy surfaces for GeC have been examined by the full valence configuration interaction technique to search for a possible transition state that might explain this discrepancy. However, it has been found that both states smoothly dissociate to the ground P-3 states of carbon and germanium without any transition state. Several theoretical and experimental aspects related to the determination of the dissociation energy of GeC have been discussed. It is concluded that the theoretically determined value of 91.4 kcal/mol should be more reliable than the reported experimental values. (C) 2003 American Institute of Physics.