Key properties of nanocrystals are determined by their real atomic structure, therefore a reasonable understanding and meaningful interpretation of their properties requires a realistic model of the structure. In this paper we present an evidence of a complex response of the lattice distances to external pressure indicating a presence of a complex structure of SiC nanopowders. The synchrotron and neutron powder diffraction experiments were performed on nanocrystalline SiC subjected to hydrostatic or isostatic pressure. Elastic properties of the samples were examined based on X-ray diffraction data using a Diamond Anvil Cell (DAC) in HASYLAB at DESY. The dependence of the lattice parameters and of the Bragg reflections width with pressure exhibits a dual nature of the properties (compressibilities) of the powders and indicates a complex structure of the grains. We interprete this behaviour as originating from different elastic properties of the grain interior and surface. Analysis of the dependence of individual interatomic distances on pressure was based on in-situ neutron diffraction measurements done with HIPD diffractometer at LANSCE in Los Alamos National Laboratory with the Paris-Edinburgh cell under pressures up to 8 GPa (Qmax = 26 A^-1). Interatomic distances were obtained by PDF analysis using the PDFgetN program. We have found that the interatomic distances undergo a complex, non-monotonic changes. Even under substantial pressures a considerable relaxation of the lattice may take place: some interatomic distances increase with an increase in pressure. We relate this phenomenon to (i), changes of the microstructure of the densified material, in particular breaking of its fractal chain structure and, (ii), its complex structure resembling that of a material composed of two phases, each with its distinct elastic properties.