Nonconvex　minimax　problems　frequently　arise　in　machine　learning,　distributionally　robust　optimization,　and　many　other　research　fields.　In　this　paper,　we　propose　a　Stochastic　Alternating　Mirror　Descent　Ascent　with　Momentum　(SAMDAM)　algorithm　to　solve　nonconvex-strongly　concave　minimax　optimization　problems.　SAMDAM　employs　simple　mirror　descent　ascent　steps　along　with　momentum　acceleration　to　update　the　variables　\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$x$$\end{document}　and　\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$y$$\end{document}　alternately　at　each　iteration.　We　further　prove　that　SAMDAM　achieves　a　gradient　complexity　of　\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$\mathcal{O}(\kappa＜^＞{3}\epsilon＜^＞{-4})$$\end{document}　for　finding　an　\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$\epsilon$$\end{document}-stationary　point　in　stochastic　nonconvex　settings,　where　\documentclass[12pt]{minimal}　\usepackage{amsmath}　\usepackage{wasysym}　\usepackage{amsfonts}　\usepackage{amssymb}　\usepackage{amsbsy}　\usepackage{mathrsfs}　\usepackage{upgreek}　\setlength{\oddsidemargin}{-69pt}　\begin{document}$$\kappa$$\end{document}　represents　the　condition　number　of　the　problem.　Finally,　computational　experiments　demonstrate　that　SAMDAM　outperforms　several　state-of-the-art　algorithms　in　distributionally　robust　optimization　and　fair　classification　tasks.