Abstract Photonic crystals and hyperbolic metamaterials are merged to give the concept of photonic hypercrystals. It combines the properties of its two constituents to give rise to novel phenomena. Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation. Both dielectric and metallic photonic hypercrystals are studied and it is found that nonlinearity limits the infinite divergence of wave vectors of the surface waves. These states exist in the frequency region where the linear surface waves do not exist. It is also shown that the nonlinearity can be used to engineer the group velocity of the resulting surface wave.