  Recent experiments have established a type of nonsymmorphic symmetry
protected nodal lines in the family of two-dimensional (2D) composition tunable
materials NbSi$_x$Te$_2$. Here, we theoretically study the plasmonic properties
of such nonsymmorphic nodal-line semimetals. We show that the nonsymmorphic
character endows the plasmons with extremely strong anisotropy. There exist
both intraband and interband plasmon branches. The intraband branch is gapless
and has a $q^{1/2}$ dispersion. It is most dispersive and is independent of
carrier density in direction normal to the nodal line, whereas along the nodal
line, its dispersion is largely suppressed and its frequency scales linearly
with carrier density. The interband branches are gapped and their long
wavelength limits are connected with van Hove singularities of the band
structure. We find that the single particle excitations are strongly suppressed
in such systems, which decreases the Landau damping of plasmons. These
characters are further verified by first-principles calculations on 2D
NbSi$_x$Te$_2$. Interesting features in static screening of charged impurity
are also discussed. Our result reveals characteristic plasmons in a class of
nonsymmorphic topological semimetals and offers guidance for its experimental
detection and possible applications.
