The correlation function of translational diffusion of molecules adsorbed in a monomolecular surface layer is determined by the restriction of molecular mobility. Using the two-dimensional diffusion equation the calculation of the correlation function g(τ) yields a very low decrease. In addition to one must consider the exchange of molecules with the gas phase in the correlation function. As g(τ) cannot be presented by elementary functions further results are obtained by means of numerical calculations and according to that the spectral density of two-dimensional translational diffusion is determined. Using this spectral density the dependence of relaxation times T1 and T2 on the diffusion correlation time τc and on the life time τh of molecules in the surface phase is discussed. The ratio T1: T2 is shown to depend on the parameter α = τc/τh strongly. The corresponding frequency and temperature dependence of T1 and T2 respectivly are investigated.