The problem of monitoring the structural and morphological evolutions of thin films of organic molecular materials during their growth by organic molecular beam epitaxy and in the postgrowth stage is addressed here by a combination of in situ optical reflectance anisotropy measurements, ex situ optical and morphological investigations, and theoretical simulation of the material optical response. For alpha-quaterthiophene, a representative material in the class of organic molecular semiconductors, the results show that molecules crystallize in the first stage of growth in metastable structures, even when deposition is carried out at room temperature. In the postdeposition stage, the film structure evolves within a few days to the known equilibrium structure of the low temperature polymorph. When deposition is carried out at low substrate temperatures, an evolution of the film morphology is also demonstrated.