  Using the spectroscopic imaging capabilities of the Swedish Solar Telescope,
we aim to provide the first investigation on the nature and dynamics of
elongated absorption features (fibrils) observed in H$\alpha$ in the
internetwork. We observe and identify a number of internetwork fibrils, which
form away from the kilogauss, network magnetic flux, and we provide a synoptic
view on their behaviour. The internetwork fibrils are found to support
wave-like behaviour, which we interpret as Magnetohydrodynamic (MHD) kink
waves. The properties of these waves, that is, amplitude, period, and
propagation speed, are measured from time-distance diagrams and we attempt to
exploit them via magneto-seismology in order to probe the variation of plasma
properties along the wave-guides. We found that the Internetwork (IN) fibrils
appear, disappear, and re-appear on timescales of tens of minutes, suggesting
that they are subject to repeated heating. No clear photospheric footpoints for
the fibrils are found in photospheric magnetograms or H$\alpha$ wing images.
However, we suggest that they are magnetised features as the majority of them
show evidence of supporting propagating MHD kink waves, with a modal period of
$120$~s. Additionally, one IN fibril is seen to support a flow directed along
its elongated axis, suggesting a guiding field. The wave motions are found to
propagate at speeds significantly greater than estimates for typical
chromospheric sound speeds. Through their interpretation as kink waves, the
measured speeds provide an estimate for local average Alfv\'en speeds.
Furthermore, the amplitudes of the waves are also found to vary as a function
of distance along the fibrils, which can be interpreted as evidence of
stratification of the plasma in the neighbourhood of the IN fibril.
