Anisotropic crystalline potentials for N2and O2trapped in β-quinol clathrates have been deduced from atom-atom Lennard-Jones and electrostatic multipolar potentials. It was made clear that the multipolar interactions due to the hydroxyl groups and benzene rings constituting the cage of β-quinol are essential. The dipole moment of the OH group has been estimated by use of an obtained theoretical relation between the dipole and quadrupole moments of the atomic groups, μOH= 0·1233 ¢ 108Q2benzene+ ξ, where the value of ξ was determined from magnetic resonance data on zero-point libration. According to recent N.Q.R. data of N2, one has μOH= 0·96 × 10-18e.s.u. cm forQ2benzene= -5·6 × 10-26e.s.u. cm2. The temperature dependence of the order parameter for molecular orientation was also examined. The calculated order parameter was found to be in good agreement with experimental one in the case of N2, and the E.P.R. case of O2was predicted.