We study the existence of normalized solutions for the following Choquard system: \(\begin{aligned} \left\{ \begin{aligned}&-\Delta u + \lambda _1 u = \left( I_\alpha *F(u)\right) f(u) + \beta \partial _u H(u,v), & \text { in } \mathbb {R}^2,\\&-\Delta v + \lambda _2 v = \left( I_\alpha *G(v)\right) g(v) + \beta \partial _v H(u,v), & \text { in } \mathbb {R}^2,\\&\int _{\mathbb {R}^{2}} {|u|^2}\,\textrm{d} x = a^2, \int _{\mathbb {R}^{2}} {|v|^2}\,\textrm{d} x = b^2, \end{aligned}\right. \end{aligned}\) where \(a, b > 0 \) , \(\alpha \in (0, 2) \) and \(\beta > 0 \) . Here, f, g have an exponential critical growth, H is a Carathéodory function, \(F(t):= \int _0^{t}{f(s)}\,\textrm{d} s \) and \(G(t):= \int _0^{t}{g(s)}\,\textrm{d} s \) . \(I_\alpha \) is the Riesz potential and \(\lambda _1, \lambda _2 \in \mathbb {R}\) appear as unknown Lagrange multipliers. We focus on the coupled pure mass super-critical case and establish the existence of normalized mountain pass solution for all \(a, b > 0\) . Under some further assumptions, the normalized ground state solution is also obtained.
