This paper studies the existence of electromagnetic surface waves localized on a boundary of half-infinite periodic superlattices formed by an arbitrary periodic sequence of layers of homogeneous or functionally graded materials with generally anisotropic dielectric permittivity and magnetic permeability tensors. The geometry in question implies either two superlattices attached together to form a photonic bicrystal or else a superlattice in contact with vacuum or any other homogeneous dielectric or metal. Using the formalism of transfer and impedance matrices, a series of statements is proved on the maximum number of surface waves which may exist within a forbidden band at a fixed tangential wave number. This number embraces possible occurrences of surface waves in a given bicrystal and in its counterpart obtained by swapping the upper and lower superlattices. A maximum total number of surface waves in both these structures with an arbitrary arrangement of their unit cells is 2 in the lowest forbidden band (extending from zero frequency) and 4 in any upper forbidden band. The same statements apply to the case where one of the half spaces is occupied by a homogeneous material. A factor 2 smaller number of surface waves occur in a bicrystal composed of superlattices with a symmetric arrangement of unit cells. The existence considerations are further specialized for the surface waves with TE and TM polarizations.Read less <