  We investigate the pattern of asymmetries in the colour-octet model for
inclusive production of charmonium with polarised initial state hadrons and
photons. We find that singly polarised asymmetries vanish. The double polarised
asymmetry for J/psi involves a new combination of long-distance matrix element.
We also investigate the asymmetries for eta_c, chi_c and Upsilon production.
The asymmetries distinguish well between different models of charmonium
production.
