At the cooler synchrotron COSY, polarized protons and deuterons are accelerated up to 3.65 GeV/c. In a strong‐focusing synchrotron like COSY, imperfection and intrinsic resonances cause polarization losses during acceleration. During the acceleration of polarized protons, five imperfection resonances are crossed. The existing magnet system of COSY allows to overcome all imperfection resonances by exciting adiabatic spin flips without polarization losses. The number of intrinsic resonances depends on the superperiodicity of the lattice. A tune‐jump system consisting of two fast quadrupoles has been developed to handle intrinsic resonances in COSY. Vertically polarized proton beams with more than 75&percent; polarization have been delivered in recent years to internal as well as to external experiment areas at different momenta up to the maximum momentum of COSY. For the acceleration of polarized deuterons, additional correction provisions are not necessary to preserve polarization during acceleration. In this paper the techniques to overcome depolarizing resonances and the status of the polarized beam acceleration at COSY are discussed. © 2003 American Institute of Physics