The spin program at the NICA collider is under preparation. The purpose of this program is the study of the nucleon spin structure and other phenomena with polarized proton and deuteron beams. Our project focuses on the very interesting possibilities provided by the second collider option with the light nuclear beams, in particular with the proton and deuteron ones. It is argued that the design of the collider should allow to reach the collision proton energy up to √s ≈26 GeV with the average luminosity up to 2.1030 cm2/s, and for the deuteron collisions - up to √s ≈12 GeV per nucleon with the average luminosity up to 1029cm2/s. It is of great importance that both proton and deuteron beams can be effectively polarized longitudinally and transversally.