The physics of polarized nucleon--nucleon collisions originating from an internal polarized target in the HERA proton beam is investigated. Based on 240 pb~-1 integrated luminosity at 40 GeV c.m. energy, statistical sensitivities are given over a wide (x_F, p_T) range for a variety of inclusive and exclusive final states. By measuring single spin asymmetries unique information can be obtained on higher twist contributions and their p_T-dependence. From double spin asymmetries in both photon and J/psi production it appears possible to measure the polarized gluon distribution in the range 0.1<x_gluon<0.4 with a good statistical accuracy.