  On the one hand, we investigate the Bahadur representation for sample
quantiles under $\varphi$-mixing sequence with $\varphi(n)=O(n^{-3})$ and
obtain a rate as $O(n^{-\frac{3}{4}}\log n)$, $a.s.$. On the other hand, by
relaxing the condition of mixing coefficients to
$\sum\nolimits_{n=1}^\infty\varphi^{1/2}(n)<\infty$, a rate $O(n^{-1/2}(\log
n)^{1/2})$, $a.s.$, is also obtained.
