Highly ordered monolayers of two perylene derivatives (perylene-3,4,9,10-tetracarboxylic-3,4,9, 10-dianhydride (PTCDA) and N,N'-dimethylperylene-3,4,9,10-bis(dicarboximide) (DM-PBDCI)) were prepared by vacuum sublimation on Ag(111) and Ag(110) surfaces. Using scanning tunnelling microscopy (STM) and low energy electron diffraction, the nucleation, growth, step site interaction. and superstructures were investigated and compared. All adsorbate structures are commensurate, with the exception of DM-PBDCI on Ag(111). A similar, but not identical, submolecular STM resolution was obtained for both molecules and on both surfaces. The local distribution shows ten dominant intensity maxima per molecule and corresponds to that of the lowest unoccupied orbital. From these results we draw conclusions concerning the tunnelling mechanism, the adsorbate-substrate, and the adsorbate-adsorbate interactions, which are discussed in relation to the formerly published results on the electronic structure of PTCDA/Ag(111). (C) 1998 Elsevier Science B.V. All rights reserved.