  We consider double spin asymmetries for longitudinally polarized leptons and
transversely polarized protons in diffractive vector meson and $Q \bar Q$
production at high energies within the two-gluon model. The asymmetry predicted
for meson production is quite small. The $A_{lT}$ asymmetry for $Q \bar Q$
production contains two independent terms which are large and can be used to
obtain information on the polarized gluon distributions in the proton.
