  We study theoretically two-photon states in a periodic array of coupled
cavities with both on-site and nonlocal Kerr-type nonlinearities. In the
absence of nonlinearity the structure is topologically trivial and possesses no
edge states. The interplay of two nonlinear interaction mechanisms described by
the extended Hubbard model facilitates formation of edge states of bound photon
pairs. Numerical and exact analytical results for the two-photon wave functions
are presented. Our findings thus shed light onto the edge states of composite
particles and their localization properties.
