It is well known that the s-stage Gauss Runge-Kutta methods of order 2s are algebraically stable, or equivalently (1, 0)-algebraically stable. In this paper, we show that there exists some ls > 0 such that the Gauss methods are (k, l) algebraically stable for l ε [0, ls) with k(l)=e2l+O(lp+1, where p=2s if s=1 or s=2, and p=2 if s>3.