The nucleation and growth of hydrate on the surface of ice was followed by NMR spectroscopy using hyperpolarized Xe. From the ice surface area and Xe pressure drop, the thickness of the hydrate film formed was similar to 500-1000 Angstrom before the reaction became extremely slow, The cage occupancy ratio theta (L)/theta (S) was measured as a function of time from the Xe spectrum and was used to monitor the nature of the material formed. The ratio changed from values close to 1 during the early part of the reaction (induction time) to its equilibrium value of similar to3-4 after nucleation processes were finished and rapid growth commenced. The low value can be seen as evidence of a precursor phase that is quite different from the equilibrium hydrate. The induction time was found to be a reproducible function of temperature and pressure for the conditions studied. The kinetics of gas uptake was analyzed according to the Avrami-Erofeyev equation used to describe solid-gas reactions. A surface memory effect was noted on successive cycles of xenon adsorption-desorption-readsorption, as the induction time was absent on the readsorption cycle. The now results are discussed in terms of models for nucleation and growth of hydrate and the various experiments that have been carried out in the past. It is essential to differentiate between later-stage diffusion-limited hydrate formation processes and the initial steps of hydrate formation at a surface, as they have opposite temperature coefficients.