  Two-spin asymmetries $A_{LL}^{\pi^0}$ are calculated for various types of
spin-dependent gluon distributions. It is concluded that the E581/704 data on
$A_{LL}^{\pi^0}$ do not necessarily rule out the large gluon polarization but
restrict severely the $x$ dependence of its distribution. Moreover,
$A_{LL}^{J/\psi}$ are calculated for the forthcoming test of spin-dependent
gluon distributions.
