In this paper, we give a general decay rate for a quasilinear para-bolic viscoelatic system under a general assumption on the relaxation functionssatisfying g'(t)≤ξ(t)H(g(t)), where H is an increasing, convex function andξ is a nonincreasing function. Precisely, we establish a general and optimaldecay result for a large class of relaxation functions which improves and gener-alizes several stability results in the literature. In particular, our result extendsan earlier one in the literature, namely, the case of the polynomial rates whenH(t) = t~p; t ≥ 0; (A)p > 1, instead the parameter p ∈ 1; 3/2 .
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