  We argue that the production of forward jets in polarised deep inelastic
scattering can be a useful tool for probing the double $ln^2(1/x)$ resummation
effects which control the polarised deep inelastic scattering for small values
of the Bjorken parameter $x$. We solve the corresponding integral equations
generating the double $ln^2(1/x)$ resummation and calculate the differential
structure function describing the forward jet production in the small $x$
regime which can possibly be probed by the polarised HERA measurements. We show
that these structure functions should exhibit the characteristic increase with
decreasing $x/x_J$, where $x_J$ denotes the longitudinal momentum fraction of
the parent proton carried by a jet, and we quantify this increase.
