Asymptotic h-expansiveness for amenable group actions can be introduced respectively using topological conditional entropy by Chung-Zhang in [J. Funct. Anal. 268 (2015), no. 11, 3534–3565] and using entropy structure by Downarowicz-Zhang in [Memoirs Amer. Math. Soc., to appear]. In this talk we will show the equivalence of these two kinds of asymptotic h-expansiveness. This is a joint work with T. Downarowicz from Poland.