The pentadecanoic acid-heptadecanoic acid (C(15)H(29)OOH-C(17)H(33)OOH) binary system is dealt with in this article. Combined thermal analysis and X-ray powder diffraction experiments are performed to characterize the polymorphism of the pure compounds and of their mixed samples. In particular, modern methods of crystal structure resolution from powder data (direct space methods) are applied in order to investigate and compare the molecular arrangement within the solid phases of the fatty acids considered. A proposal of the binary phase diagram is given. It exhibits no less than eight distinct solid phases stabilized on relatively narrow domains of composition which shows the reduced miscibility of the constituents. Finally, a structural model of one of the intermediate solid solutions is developed which well accounts for the mixing behaviour of the two fatty acids and permits to propose an explanation about their low solid-state miscibility.