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In this paper, we consider the product-limit quantile estimator of an unknownquantile function under a censored dependent model. This is a parallel problemto the estimation of the unknown distribution function by the product-limitestimator under the same model. Simultaneous strong Gaussian approximations ofthe product-limit process and product-limit quantile process are constructedwith rate $O((\log n)^{-\lambda})$ for some $\lambda>0,$. The strong Gaussianapproximation of the product-limit process is then applied to derive the lawsof the iterated logarithm for product-limit process.

Strong Gaussian approximations of product-limit and Quantile Processes for Strong mixing and censored data