The precise description of evolution processes is one of the most important problems in the field of nanoscience. Especially there are specific nonequilibrium corporative phenomena of self-assembling and self-organization. In present work the problem of nonequilibrium corporative algorithmic motion of nanosystems is investigated. As regards the corporative motion, it is observed both in equilibrium and in non-equilibrium electron-nuclear systems. In the former this results in the existence of adiabatic lattice of nuclei and phonon acoustic modes, whereas in the latter corporative effects involve non-adiabatic algorithmic processes including self-assembly and self-organization, generating nanostructures. Initialization such kind operations require at least three conditions: (a) nonequilibrium, (b) corporative and (c) algorithmic dynamics of nanosystem. The fundamental scheme of evolution is considered as applied to nonequilibrium nanosystems, whose discontinuous and non-adiabatic motion in configuration space is controlled by quantum correlations with topologic structures of Bose-condensate vacuum states of physical fields. By the example of nickel and graphene nanoparticles it is investigated time-dependent algorithmic behavior of consolidated quantum-sized field systems. It is shown that time quanta of discrete nanoparticle transformations amounts to a femtosecond. Today femtosecond and sub-femtosecond range turns out to be beyond resolution power of the up-to-date devices of nanotechnology. In the circumstances it is really significant to know the availability of theoretical approaches, used for description of the nanoscale dynamics. The model considered allows one to forecast the discrete forms of nanoparticle structural organization under variable experimental conditions. This, in turn, clears the way to directional effect on widely applicable structures in technologies and industry practice for the purpose of control the nanoparticle femtosecond dynamics.