Discusses the equilibrium configurations and the phase transitions of a semi-classical model system consisting of two equal magnetic moments coupled by isotropic, anisotropic and antisymmetric exchange, with uniaxial anisotropy terms up to fourth order, in the presence of a transverse magnetic field. No restriction is imposed on the values of the interaction parameters. Magnetic configurations of the 'conical' type appear for non-negligible values of the antisymmetric exchange and of the fourth-order anisotropy term, and are found to be stable over a wide range of values of the physical parameters and the external field. The results of the theoretical model are applied to the interpretation of the neutron scattering data and the transverse magnetisation measurements on some diamagnetically substituted hexaferrites of the Y and Z types.