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Multifold degenerate fermions have attracted a lot of research interest in condensed matter physics and materials science, but always lack in two dimensions. In this Letter, from symmetry analysis and lattice model construction, we demonstrate that eightfold degenerate fermions can be realized in two-dimensional systems. In nonmagnetic materials with negligible spin-orbit coupling, the gray magnetic space groups together with SU(2) spin rotation symmetry can protect the two-dimensional eightfold degenerate fermions on a certain high-symmetry axis in the Brillouin zone, no matter whether the system is centrosymmetric or noncentrosymmetric. In antiferromagnetic materials, the eightfold degenerate fermions can also be protected by certain "spin space groups." Furthermore, by first-principles electronic structure calculations, we predict that the paramagnetic phase of the monolayer LaB_{8} on a suitable substrate is a two-dimensional eightfold degenerate as well as Dirac node-line semimetal. Especially, the eightfold degenerate points are close to the Fermi level, which makes monolayer LaB_{8} a good platform to study the exotic physical properties of two-dimensional eightfold degenerate fermions.

By combining angle-resolved photoemission spectroscopy and quantum oscillation measurements, we performed a comprehensive investigation on the electronic structure of LaSb, which exhibits near-quadratic extremely large magnetoresistance (XMR) without any sign of saturation at magnetic fields as high as 40 T. We clearly resolve one spherical and one intersecting-ellipsoidal hole Fermi surfaces (FSs) at the Brillouin zone (BZ) center Γ and one ellipsoidal electron FS at the BZ boundary X. The hole and electron carriers calculated from the enclosed FS volumes are perfectly compensated, and the carrier compensation is unaffected by temperature. We further reveal that LaSb is topologically trivial but shares many similarities with the Weyl semimetal TaAs family in the bulk electronic structure. Based on these results, we have examined the mechanisms that have been proposed so far to explain the near-quadratic XMR in semimetals.