A relaxation of small metal nanoparticles is considered within the computer simulation of quantum evolution kinetics of NEMS. The objects of research in this paper are the perfect cuboids of FCC-lattice of Cu and Fe, bounded by (100)-type planes, and containing 172 atoms. Calculations are performed for a temperature of 293K. The set of computer simulations demonstrates that the relaxation evolution of such particles from pulse excited nonequilibrium states has specific features of behavior and diversity of structural states. A possibility of self-organization process progressing through several intermediate metastable states of nanosystems is revealed. A set of possible nanosystems configurations in the overall picture of their evolution is obtained. It is shown that on the first stage of relaxation, the leading process is an all-round expansion of NEMS cuboids for the iron case and compression for the copper case with the transformation of the cube into a spheroid. In the case of iron, the first transformation of a cube into cuboid is determined by bending of NEMS cube surface faces, and the second transformation goes with a change of faces into trapezoids. In the case of copper, cuboid faces appear from the spheroid in the second transformation. At the third transformation of copper, cuboid faces are distorted, but there is no trapezoid stage. It is shown that final stages of restructuring with a final attractor stable structure formation covers all atomic layers of NEMS cuboid equally. This is the fundamental difference of relaxation of NEMS from clusters of atoms in a gas.