In a preceding paper the theory of the intermolecular NMR-relaxation of molecules adsorbed on solid surfaces was developed. This former treatment which was based on the diffusion equation is extended to processes with finite jumping lengths of the molecules along the surface. T1 is given as a function of the jumping time τv for different jumping lengths and it is shown that the shape of T1-curve at the minimum depends strongly on the length of the jumps. In addition to this the temperature dependence of T2 as a function of the length of jumps and of the life-times of the molecules on the surface respectively is discussed. The theoretical results allow to explain the measurements of the intermolecular NMR-relaxation times of benzene and methane adsorbed on silicagel by MICHEL and BECKERT respectively.