We present 77Se NMR measurements in EuSe and review previous 153Eu NMR measurements that show that EuSe displays 2D characteristics at both ends of the magnetization curve. The lowtemperature behavior, in agreement with previous measurements, follows a simple 2D T2 falloff. At the higher temperatures, a critical-exponent fit shows an apparent 2D behavior with ß ~ 0.18 ± 0.02. EuSe has always appeared to be a complicated magnetic system, with a number of co-existing magnetic phases and an alleged first-order magnetic transition. We argue that the multiple magnetic structures are in fact compatible with 2D behavior, and that there is actually no firm evidence of a first-order transition. In the ferromagnetic state of EuSe (obtained under pressure or by an applied field), a ß ~ 0.33 is found, but with a D ~ 1, characteristic of the behavior of the classic 2D magnets K2CuF4 and CrCl3, and not of 3D critical behavior. Additional experiments to verify the 2D nature of EuSe are suggested. The nontrivial implications of the two-dimensionality of EuSe regarding the nature of magnetic interactions in general are also discussed.