Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(x, t)=v (cl--X) are called W soIutiOns if there exjstS a fwite ', such that u({)=v(j)=0 for t<{,':=ct--x. It is proVed that if Pq+nl l. The asmpptohc weve profileS near the front as well as far from it are also determined. If I)q^m = l. the exjstence of travebe wave soluhons to (I) is proved. The plnof in Esqniruis's paper(1990) for the one m=0 co be sdriplified by using the methOd develOped in thjs paper.
