  In this paper we study spatial analyticity of solutions to the defocusing
nonlinear Schr\"odinger equations $iu_t + \Delta u = |u|^{p-1}u$, given initial
data which is analytic with fixed radius. It is shown that the uniform radius
of spatial analyticity of solutions at later time $t$ cannot decay faster than
$1/|t|$ as $|t|\rightarrow\infty$. This extends the previous work of Tesfahun
for the cubic case $p=3$ to the cases where $p$ is any odd integer greater than
$3$.
