We study non-Hermitian higher-order Weyl semimetals (NHHOWSMs) possessing real spectra and having inversion $\mathcal{I}$ ($\mathcal{I}$-NHHOWSM) or time-reversal symmetry $\mathcal{T}$ ($\mathcal{T}$-NHHOWSM). When the reality of bulk spectra is lost, the NHHOWSMs exhibit various configurations of surface Fermi arcs and exceptional Fermi rings (EFRs), providing a setup to investigate them on an equal footing. The EFRs only appear in the region between second-order Weyl nodes. We also discover Weyl nodes originating from non-Hermiticity, called non-Hermitian Weyl nodes (NHWNs). Remarkably, we find $\mathcal{T}$-NHHOWSMs which host only second-order NHWNs, having both surface and hinge Fermi arcs protected by the quantized biorthogonal Chern number and quadrupole moment, respectively. We call this intrinsically non-Hermitian phase exceptional HOWSM. In contrast to ordinary Weyl nodes, the NHWNs can instantly deform to line nodes, forming a monopole comet. The NHWNs also show exceptional tilt rigidity, which is a strong resistance towards titling due to attachment to exceptional structures. This phenomenon can be a promising experimental knob. Finally, we reveal the exceptional stability of Fermi arcs called exceptional helicity. Surface Fermi arcs having opposite chirality can live on the same surface without gapping out each other due to the complex nature of the spectrum. Our work motivates an immediate experimental realization of NHHOWSMs.

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• Topological phases of matter
• Topological materials
• Weyl semimetal