The possibility of accelerating polarized deuterons in the AGS and RHIC is discussed. In the AGS, the polarized deuteron can be accelerated up to 15 GeV/c without depolarization. In RHIC, the snake designed for use in accelerating polarized protons are applicable as partial snake in inducing spin flip to overcome the imperfection resonances. Gradient error resonances in RHIC are found to be negligible. Difficulties arise from intrinsic resonances in RHIC, which limit the polarized deuteron collision energy to less than &ggr;≤29 or to energy less than 27.2 GeV/u, if corrections are not made. A type 3 snake is found to be impractical for a spin tune jump. Betatron tune jump by using quadrupoles or induced betatron oscillations may be used to jump through intrinsic resonances. The achievable luminosity is found to about 2⋅1030cm−2s−1at &ggr;≊30. If intrinsic resonances can be overcome, one expects to obtain higher energy and higher luminosity.