[en] The first part of this thesis is an experimental investigation of the interaction responsible for the I-II transition and the second part comprises three theoretical studies of several of the properties of phase I and II. The first chapter of part I, is a general introduction to a thermodynamic treatment of the isotope effect in an orientational phase transition. The thermodynamic approach yields a corresponding state model for the phase diagrams of the five isotopes of methane (CH₄, CHD₃, CH₂D₂, CH₃D and CD₄). In the remaining two chapters of part I, the corresponding state relation mentioned above is applied to the I-II transition of methane in order to obtain an experimental value for the effective exponent n of the dependence on intermolecular separation of the ordering anisotropic interaction. Part II starts with a derivation of a quasi-classical approximation to the statistical density matrix of a free spherical top. While the orientational system is treated classically, the consequences of the other characteristic of the methane molecules are considered, i.e. the high approximately odd symmetry of the molecule (the octupole field in phase II is odd under spatial inversion). It is argued that the renormalization group analysis of critical phenomena in certain highly complicated antiferromagnetic systems may be equally well applied to the I-II transition in methane. Finally, the study of the quantum effect in phase II is resumed. The spin lattice relaxation time at very low temperature is calculated from first principles using an orientational dynamical process of purely quantum-mechanical nature. (Auth.)