In the paper we consider a tensor sum H µ,λ , µ, λ > 0 of two Friedrichs models h µ,λ with rank two perturbation. The Hamiltonian H µ,λ is associated with a system of three quantum particles on one-dimensional lattice. We investigate the number and location of the eigenvalues of H µ,λ . The existence of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of H µ,λ is proved. KEYWORDS tensor sum, Hamiltonian, lattice, quantum particles, non-local interaction, Friedrichs model, eigenvalue, perturbation. ACKNOWLEDGEMENTS The authors thank the anonymous referee for reading the manuscript carefully and for making valuable suggestions. FOR CITATION Rasulov T.H., Bahronov B.I. Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation.