  We discuss the double-spin asymmetries in transversely polarized Drell-Yan
process, calculating all-order gluon resummation corrections up to the
next-to-leading logarithmic accuracy. This resummation is relevant when the
transverse-momentum Q_T of the produced lepton pair is small, and reproduces
the (fixed-order) next-to-leading QCD corrections upon integrating over Q_T.
The resummation corrections behave differently between pp- and
p\bar{p}-collision cases and are small for the latter case at the kinematics in
the proposed GSI experiments. This fact allows us to predict large value of the
double-spin asymmetries at GSI, using the recent empirical information on the
transversity.
