  Non-Hermitian (NH) Hamiltonians have become an important asset for the
effective description of various physical systems that are subject to
dissipation. Motivated by recent experimental progress on realizing the NH
counterparts of gapless phases such as Weyl semimetals, here we investigate how
NH symmetries affect the occurrence of exceptional points (EPs), that
generalize the notion of nodal points in the spectrum beyond the Hermitian
realm. Remarkably, we find that the dimension of the manifold of EPs is
generically increased by one as compared to the case without symmetry. This
leads to nodal surfaces formed by EPs that are stable as long as a protecting
symmetry is preserved, and that are connected by open Fermi volumes. We
illustrate our findings with analytically solvable two-band lattice models in
one and two spatial dimensions, and show how they are readily generalized to
generic NH crystalline systems.
