  We calculate the double-spin transverse asymmetries for the Drell-Yan lepton
pair production in p-p and p-anti p collisions. We assume the transverse and
the longitudinal polarization densities to be equal at a very small scale, as
it is suggested by confinement model results. Using a global fit for the
longitudinal distributions, we find transverse asymmetries of order of 10^-2 at
most, in the accessible kinematic regions.
