The large time behaviors are studied to the initial - boundary problems of 2x2 nonlinear hyperbolic system of conservation laws with relaxation and 2x2 nonlinear system of viscoelasticity in this thesis 本文研究具有松弛源项的2 2非线性双曲守恒组和2 2非线性粘弹性方程组的初边值问题解的大时间性态。