Nuclear magnetic relaxation times T and T2 have . 1 3 been measured at IMHz and 2MHz for He adsorbed on Grafoil for coverages between O. 1 and 1. 2 monolayers. Results indicate that for low coverages the film has a high mobility while at high coverages it behaves like a solid with Quantum Tunneling. Most of the data can be explained in terms of dipole - dipole interaction and interaction of the spins with the local fields in the Grafoil. The theory of relaxation in two - dimensional systems by these mechanisms is presented