  Quantum analogues of the homogeneous spaces $\GL(n)/\SO(n)$ and
$\GL(2n)/\Sp(2n)$ are introduced. The zonal spherical functions on these
quantum homogeneous spaces are represented by Macdonald's symmetric polynomials
$P_{\ld}=P_{\ld}(x_1,\cdots,x_n;q,t)$ with $t=q^{1 \over 2}$ or $t=q^2$.
