The potential energy surfaces for the low-lying electronic states of the zirconium carbon monoxide (ZrCO) and hafnium carbon monoxide (HfCO) systems have been studied using the complete active space multiconfiguration self-consistent field followed by multireference singles + doubles configuration interaction. Spin-orbit effects are included through the relativistic configuration interaction method. Ln contrast to HfCO, which exhibits a (3) Sigma(-) ground state, two nearly degenerate electronic states ((5) Delta, (3) Sigma(-)) were found as candidates for the ground state of ZrCO. Both Hf and Zr form stable complexes with CO relative to the dissociation limits. The nature of bonding is discussed in terms of the wave function composition and the Mulliken population analysis.