Despite extensive study of max--min problems, convergence analysis for the challenging nonconvex--nonconcave setting remains limited. This paper addresses the convergence analysis of nonconvex--nonconcave max--min problems. A novel analytical framework is developed by employing carefully constructed auxiliary functions and leveraging two-sided Polyak--Łojasiewicz (PL) and Quadratic Growth (QG) conditions to characterize the convergence behavior. Under these conditions, it is shown that the Stochastic Alternating Gradient Descent Ascent (SAGDA) algorithm achieves a convergence rate of $\mathcal{O}\left(1/K\right)$, where $K$ denotes the number of iterations. Notably, this result matches conv... More >