Potential energy curves along the inter-planar coordinates have been calculated for the dimers of two perylene derivatives (PTCDI and PTCDA) by using MP2 and dispersion corrected DFT (DFT-D) methods with B3LYP, B97 and PBE0 density functionals. The performance of dispersion-correcting potentials (DCPs) for describing intermolecular van der Waals interactions was also tested in conjunction with PBE0 and B971 functionals. Analytical potential energy curves were derived at different levels of theory by fitting the calculated data to modified Morse, Murrell-Sorbie, Buckingham and Lennard-Jones potentials. Potential energy surfaces for the two types of dimers were explored at the PBE0-DCP/6-31+G(d,p) level of theory in order to assess the effects of geometrical perturbations (displacements and/or rotations) on the stability of the dimers. Two minima were located for each perylene derivative, depending on the starting geometries of the dimers. Inter-monomer geometrical parameters of fully and partially optimized dimeric structures, as well as their relative stability, are discussed in comparison to available experimental data and other theoretical results on these or similar compounds.