  Spin dependent structure function $g_1^{\gamma}(x,Q^2)$ of the polarised
photon is analysed within the formalism based upon the unintegrated spin
dependent parton distributions incorporating the LO Altarelli-Parisi evolution
and the double $ln^2(1/x)$ resummation at low values of Bjorken parameter x. We
analyse the effects of the double $ln^2(1/x)$ resummation on the behaviour of
$g_1^{\gamma}(x,Q^2)$ in the low x region which may be accessible in future
linear $e^+e^-$ and $e\gamma$ colliders. Sensitivity of the predictions on the
possible nonperturbative gluon content of the polarised photons is analysed.
Predictions for spin dependent gluon distribution $\Delta g^{\gamma} (x,Q^2)$
are also given.
