LiNbO3 films have been, grown on alpha Al2O3(0001) by pulsed laser deposition. Their structural aspects have been studied by using transmission electron microscopy. Different stages of the film formation have been observed : nucleation-growth of isolated pyramids limited by the {01 (1) over bar 2} faces, coalescence of the pyramids giving rise to flat aggregates and formation of continuous films. Misfit dislocations relaxing the misfit strain at the deposition temperature have been observed. However, strain states have been found. They an dependent on the film morphology : inhomogeneous elastic strain field in isolated pyramids, mechanical twinning and cracks in continuous films. It is shown that in both cases, the strain state corresponds to the relaxation of stresses occurring at the film/substrate interface during the cooling stage from deposition to room temperature, due to a large difference in thermal expansion coefficients of LiNbO3 and alpha Al2O3.