For Pt. I see ibid. vol. 4, 2127. The theory of the low lying magnetic excitations of KCoF₃ is developed and the parameters describing the magnetic interactions are obtained by comparison with the experimental results of the previous paper. The branch of the elementary excitation spectrum of lowest frequency is well described by a phenomenological model with an effective spin s'=¹/₂. The exchange interaction has the Heisenberg form, and the pseudo-dipolar form of anisotropic exchange proposed for KCoF₃ is shown to be less than 8% of the isotropic exchange. A model which takes the orbital angular momentum of the Co²⁺ ion into account is developed by relating the elementary excitations to the quasiboson excitations between the ground state and all eleven excited states of the ⁴T₁ orbital level. This model fits the experimental results for the two branches of lowest frequency extremely well. The interaction between real spins is found to of the Heisenberg form and the spin-orbit coupling constant is found to be 82% of the free ion value. Calculations of the relative intensity of neutron scattering as a function of wavevector transfer for the modes belonging to the two lowest branches of magnetic excitations give good agreement with experiment.