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Metal-insulator (CoFeB) x (LiNbO 3 ) 100−x nanocomposite films with different content of the ferromagnetic (FM) phase x are investigated by ferromagnetic resonance (FMR) technique. A strong change of the FMR line shape is observed in the vicinity of metal-insulator transition (MIT) of the film, where the hopping-type conductivity σ modifies to the regime of a strong intergranular tunnelling, characterized by a logarithmic dependence σ(T ) at high temperatures. It is shown that below MIT, the FMR linewidth is mainly determined by the inhomogeneous distribution of the local anisotropy axes in the film plane. Above MIT, the contribution of this inhomogeneity to the line broadening decreases. At the same time, two-magnon magnetic relaxation processes begin to play a significant role in the formation of the linewidth. The observed behaviour indicates the critical role of interparticle exchange in the tunnelling regime above MIT of the nanocomposite.