＜正＞ This paper discusses the following initial-boundary value problems for the first orderquasilinear hyperbolic systems:（u）/（t）+A（u）（u）/（x）=0,（1）uⅡ=F（uⅠ）,as x=0,（2）uⅠ=G（uⅡ）,as x=L,（3）u=u~0（x）,as t=0,（4）where the boundary conditions（2）,（3）satisfy F（0）=0,G（0）=0 and the dissipativeconditions,that is,the spectral radii of matrices B1=（F）/（uⅠ）（0）（G）/（uⅡ）（0）and B2（G）/（uⅡ）（0）（F）/（uⅠ）（0） are less than unit.Under certain assumptions it is proved that the initial-boundary problem （1）—（4）admits a unique global smooth solution u（x,t）and the C~1-norm丨u（t）丨σ~2of u（x,t）decaysexponentially to zero as t→∞,provided that the C~1-norm丨u~0丨σ~1of the initial data issufficiently small.
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