A series of nickel-chromium-ferrite NiFe(2-)xCr(x)O(4) (with x = 1.25) nanoparticles (NPs) with a cubic spinel structure and with size d ranging from 1.6 to 47.7 nm was synthesized by the solution combustion method. A dual structure of all phonon modes revealed in Raman spectra is associated with metal cations of different types present in the spinel lattice sites. Mossbauer spectra of small NPs exhibit superparamagnetic behavior. However, the transition into the paramagnetic state occurs at a temperature that is unusually high for small particles (T-N is about 240 K in the d = 4.5 nm NPs). The larger NPs with d > 20 nm do not exhibit superparamagnetic properties up to the Neel temperature. From the magnetic and Mossbauer data, the cation occupation of the tetrahedral (A) and octahedral [B] sites was determined (Fe0.75Ni0.25)[Ni0.75Cr1.25]O-4. The saturation magnetization M-S in the largest NPs is about (0.98-0.95) mu(B), which is more than twice higher the value in bulk ferrite (Fe)[CrNi]O-4. At low temperatures the total magnetic moment of the ferrite coincides with the direction of the B-sublattice moment. In the NPs with d > 20 nm, the compensation of the magnetic moments of A- and B-sublattices was revealed at about T-com = 360-365 K. This value significantly exceeds the point T-com in bulk ferrites NiFexCr2-xO4 (about 315 K) with the similar Cr concentration. However, in the smaller NPs NiFe0.75Cr1.25O4 with d <= 11.7 nm, the compensation effect does not occur. The magnetic anomalies are explained in terms of highly frustrated magnetic ordering in the B sublattice, which appears due to the competition of AFM and FM exchange interactions and results in a canted magnetic structure.