To search for proton Electric Dipole Moments (EDM) using proton storage ring with purely electrostatic elements, the concept of frozen spin method has been proposed by Brookhaven National Laboratory. This method is based on two facts: in the equation of spin precession, the magnetic field dependence is entirely eliminated, and at the ‘‘magic’’ energy, the spin precession frequency coincides with the precession frequency of the particle momentum. In case of deuteron, we have to use the electrical and magnetic field simultaneously, keeping the frozen spin direction along the momentum as in the pure electrostatic ring. Later, Yu. Senichev proposed the concept of quasi-frozen spin, in which the spin oscillates around the direction of the pulse within half the value of the advanced phase of rotation in magnetic arcs, each time returning back in deflectors with an electrostatic field. Due to the low value of the anomalous magnetic moment of deuteron, an effective contribution to the expected EDM effect is reduced only by a few percent compared with frozen spin method. In this work, we consider the adapted structure of the NICA and Nuclotron synchrotrons, in which the ‘‘quasi-frozen spin’’ option can be implemented. The advantage of the ‘‘quasi-frozen spin’’ concept is the possibility of using synchrotrons already existing in the world that are not focused on studying EDM, which makes this method the only one possible for the accelerators of the NICA complex.