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The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we report the superuniversality notion of Anderson localization transitions in non-Hermitian two-dimensional (2D) systems with exceptional points in which the critical exponents do not depend on the symmetries. The Anderson localization transitions are numerically studied by using the finite-size scaling analysis of the participation ratios. At the exceptional points of either second-order or fourth-order, two non-Hermitian systems with different symmetries have the same critical exponent $ν\simeq 2$ of correlation lengths. This value differs from all known 2D disordered Hermitian and non-Hermitian systems. In the symmetry-preserved and symmetry-broken phases, the non-Hermitian models with time-reversal symmetry and without spin-rotational symmetry (without time-reversal and spin-rotational symmetries) are in the same universality class of 2D Hermitian electron systems of Gaussian symplectic (unitary) ensemble, where $ν\simeq 2.7$ ($ν\simeq 2.3$). The universality of the transition is further confirmed by showing that the critical exponent $ν$ does not depend on the form of disorders and boundary conditions. Our results suggest that non-Hermitian systems of different symmetries around their exceptional points form a superuniversality class.