Theoretical expectations concerning small x behaviour of the spin depe
ndent structure function g(1) are summarised. This includes discussion
of the Regge pole model predictions and of the double ln(2)(1/x) effe
cts implied by perturbative QCD. The quantitative implementation of th
e latter is described within the unified scheme incorporating both Alt
arelli-Parisi evolution and the double ln(2)(1/x) resummation. The dou
ble ln(2)(1/x) effects are found to be important in the region of x wh
ich can possibly be probed at HERA. Predictions for the polarized gluo
n distribution Delta G(x,Q(2)) at low x are also given.