Relativistic, gradient-corrected density functional theory is used to establish the equilibrium geometric structures of the title compounds. Both molecules are found to be significantly bent, with Cp*-M-Cp* angles of 160° and 154° for YbCp*2 and NoCp*2 respectively. The bent structures are calculated to be 5 (YbCp*2) and 9 (NoCp*2) kJ mol"1 more stable than the linear. The agreement between the calculated structure of YbCp*2 and that determined experimentally in the gas phase is excellent. The origins of the deviation from linearity are discussed in detail, and placed in the context of previous, contrasting explanations for bending in metallocenes. Evidence is found for both valence and core metal electron participation in the bending process. Previous implications that the Cp*2 moiety should of itself adopt a bent geometry are not supported in the present study. The metal-ligand bonding in the title compounds is found to be predominantly ionic, with small amounts of d and (to a lesser extent) f orbital covalency.