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In this paper, we investigate the long time existence and uniqueness of smallsolution to $d,$ for $d=2,3,$ dimensional Prandtl system with small initialdata which is analytic in the horizontal variables. In particular, we provethat  $d$ dimensional Prandtl system has a unique solution with the life-span ofwhich is greater than $\e^{-\f43}$ if both the initial data and the value onthe boundary of the tangential velocity of the outflow are of size $\e.$ Wemention that the tool developed in \cite{Ch04, CGP} to make the analytical typeestimates and the special structure of the nonlinear terms to this system playan essential role in the proof of this result.

Long time well-posdness of Prandtl system with small and analytic initial data