The paper analyses the laws of deformation of eutectic composites of LaB$_{6}$–TiB$_{2}$ (ZrB$_{2}$) systems with a fibrous type of hardening phase in the temperature range of 600–1600°C. The deformation mechanisms with temperature change are analysed. The low-temperature deformation mechanism is associated with the movement of dislocations in planes with maximum of reticular density and the strength of the composite in this case is determined by the reduced shear stresses in the initial slip system, the secondary slip systems and fibbers are not involved in the deformation process, the material is brittle fractured. In the case of the high-temperature deformation mechanism, LaB$_{6}$–TiB$_{2}$ (ZrB$_{2}$) composites exhibit plasticity, substructural hardening in the matrix, ductile fracture, and the density of dislocations in the fibbers increases and a substructure is formed. The temperature of the transition from low-temperature to high-temperature deformation is determined by a misfit on the matrix–fibber interface and for the LaB$_{6}$–TiB$_{2}$ composite occurs in the region of $\sim$1400°C with the misfit $\sim$1–2%, and for the LaB$_{6}$–ZrB$_{2}$ composite—at a lower temperature $\sim$1000°C with the misfit $\sim$3–4%.