Started at the beginning of the 80 th , the spin physics programme at the JINR Synchrophasotron is being continued succesfully. The next step of this programme is to accelerate of polarized beams at the Nuclotron. The first test run of polarized deuteron injection and acceleration has been carried out. The status and development of the polarized deuteron source, analysis of the depolarized effects in the linac, Nuclotron ring and beam injection/extraction transport lines are presented. Computer simulation of charge exchange injection into the accelerator is also considered.