The second part of the theory for the multicomponent nonisothermal nucleation is presented. The solution of the kinetic equation already derived in the first part is given with the help of the Chapman-Enskog procedure. At first the relaxation stage is considered. The special choice of the relaxation operator allows to refuse from the special small parameter usually required in the nucleation problems. The special procedure allows to estimate the tails of the approximations appeared in the reccurent procedures. The final formulas for corrections allows to reduce the problem to the ordinary Fokker-Planck equation in the nulticomponent case.