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　and　alternately　at　each　iteration.　We　further　prove　that　SAMDAM　achieves　a　gradient　complexity　of　for　finding　an　-stationary　point　in　stochastic　nonconvex　settings,　where　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.　©　The　Author(s)　under　exclusive　licence　to　Korean　Society　for　Informatics　and　Computational　Applied　Mathematics　2025.