The molecular order in thin films of the aromatic hydrocarbon coronene, C24H12, and its larger homologue, hexa-peri-benzocoronene ("HBC"), C42H18, obtained by vacuum-deposition onto the (0001) cleavage plane of graphite and molybdenite, MoS2, has been investigated by low-intensity low-energy electron diffraction (LEED). Under well-defined preparation conditions (low evaporation rates and moderate substrate temperatures), epitaxial films could be obtained; their epitaxial relations could be characterized by well-resolved LEED-patterns. For coverages in the monolayer region, commensurate graphite (0001)-p(square-root 21 x square-root 21 R +/- 10.9-degrees)-coronene and MoS2(0001)-p(square-root 13 x square-root 13 R +/- 13.9-degrees)-coronene superstructures are formed, while hexa-peri-benzocoronene forms commensurate graphite (0001)-p(square-root 31 x square-root 31 R +/- 9.0-degrees)-HBC and MoS2(0001)-p(square-root 21 x square-root 21 R +/- 10.9-degrees)-HBC super-structures. From the dependence of the observed superstructure lattice constants on the size and shape of the adsorbed molecules relative to the respective substrate surface lattice constants a parallel orientation of the molecular planes with respect to the substrate surface can be inferred. It is shown that under the influence of the substrate the distances and azimuthal orientations of the molecules, are determined by the closest packing permitted by their in-plane van der Waals radii. These structures are different from the respective bulk crystal structures. For the system coronene on MoS2 a model of film formation is proposed.