Density Functional Theory has been applied to the study of the molecular structure of neutral and positively charged mono- and dicarbonyls of rhodium and palladium. The calculated optimized geometries, dissociation energies and normal frequencies are reported for the MCO, MCO+, M(CO)2 and M(CO)2+ systems (where M = Rh and Pd), and the trends are discussed in detail. For neutral carbonyls, we interpret the M-C bond strength in terms of sigma repulsion, which must be avoided, and pi attraction. These are related to the metal atom properties, such as the atomic splittings and the atomic ionization energies. In ionic carbonyls, the bonding is characterized by electrostatic attraction and sigma repulsion. The rhodium carbonyls are generally found to be more stable than the corresponding palladium carbonyls. The palladium dicarbonyls are found to be linear, while both linear and bent structures are stable for rhodium dicarbonyls. An interpretation of these trends is made.