The slope-slope correlation function N(r) is investigated for self-affine rough surfaces. Calculations of N(r) are performed in terms of analytic phenomenological height-height correlation functions, which however compare well to real data. It is found that N(r) behaves as: N(r)∝r^2(H-1) for 0 « r « ξ, N(r) < 0 for r > ξ and N(r)→0- for r→+∞. The parameters ξ and H (0 < H < 1) are respectively the in-plene roughness correlation length, and the roughness exponent. Moreover, connection of the results to model predictions describing stable and unstable growth is attempted.