We present theoretical predictions for the cross sections and spin asymmetries in dilepton pair production in transversely polarized pp and p̄p collisions. We use the available fixed‐order corrections as well as the all‐order resummation of threshold logarithms for the pair mass and rapidity distributions. Numerical results for pp collisions at
at J‐PARC and for p̄p collisions at
at GSI‐PAX are given.