Using the HF, MP2, and DFT methods with a 6-311G** basis set, we examine the internal rotation and inversion of the –XH₂ group in methylamine and methylphosphine. These motions are studied by fitting the energy determined at 118 fixed geometries for methylamine and at 144 fixed geometries for methylphosphine using the two geometrical variables Φ, the dihedral angle of the lone-pair of electrons on the XH₂ group, and t, the angle between the XH₂ plane and the C-X axis. The energy surface is fit using the sums of product of Bessel functions of the first kind, J_m, and cos(mΦ). The surface depicts several special points: the three minimum energy points, the three first-order internal rotation transition points of XH₂ group about the C-X bond, the three first-order rotation-inversion transition points and the three second-order inversion transition points. For methylamine the energy barriers for pure rotation is 10.6 kJ/mol, rotation inversion is 26.2 kJ/mol and pure inversion is 29.5 kJ/mol based on MP2/B3LYP methods. For methylphosphine the energy barrier for pure rotation is 8.9 kJ/mol, rotation-inversion is 152.7 kJ/mol and pure inversion is 155.4 kJ/mol based on MP2/B3LYP method. They are in good agreement with experimental values.