Ab initio computations indicate the existence of several stable and some unstable conformers in isolated alpha and beta glucose molecules. All of the lower-energy conformers exhibit a strikingly regular pattern of internal hydrogen bonding. Five such stable structures have been identified for each of the alpha and beta anomers, differing primarily in the orientation of the. CH2OH group. In each conformer, the alpha anomer is predicted to be lower in energy than the corresponding conformers of beta anomer. The difference is about 2 kcal/mol in the 4-3 IG basis but only 0.4 kcal/mol in the 6-31G* basis. It is found that the electronic contributions to the free energy difference stabilize the alpha anomer while the nuclear motion contributions stabilize the beta anomer. The implications of these predictions and the future investigations required to understand the relative stabilities of the two anomers are pointed out.