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In this talk,I will present some recent works on the nonlinear asymptotic stability of the Lane-Emden Solutions for the Navier-Stokes-Poisson systems with positive or degenerate viscosities.This is one of the challenging problems in the theory of viscous star problems.Some of the key ideas and analysis will be discussed.These are joint works with Tao Luo and Huihui Zeng.