The main difficulties in preserving proton polarisation at adiabatic crossings of spin intrinsic resonances are related to the dependence of the resonance strength on the amplitude of betatron oscillations. There are always particles with small amplitudes in the beam, which correspond to the fast crossing of the resonance. The part of particles with fast crossing can be significantly reduced by decreasing crossing rate of the intrinsic resonance. However, synchrotron oscillations lead to splitting of the main resonance into a series of satellite resonances, the intersection of which can lead to beam depolarisation. A new method of crossing the intrinsic resonances of protons in the Nuclotron based on the suppression of the depolarising influence of satellite resonances by sextupoles is proposed.