  The recent detection of fullerene (C$_{60}$) in space and the positive
assignment of five diffuse interstellar bands to C$_{60}^+$ reinforce the
notion that fullerene-related compounds can be efficiently formed in
circumstellar envelopes and be present in significant quantities in the
interstellar medium. Experimental studies have shown that C$_{60}$ can be
readily hydrogenated, raising the possibility that hydrogenated fullerenes (or
fulleranes, C$_{60}$H$_m$, $m=1-60$) may be abundant in space. In this paper,
we present theoretical studies of the vibrational modes of isomers of
C$_{60}$H$_m$. Our results show that the four mid-infrared bands from the
C$_{60}$ skeletal vibrations remain prominent in slightly hydrogenated
C$_{60}$, but their strengths diminish in different degrees with increasing
hydrogenation. It is therefore possible that the observed infrared bands
assigned to C$_{60}$ could be due to a mixture of fullerenes and fulleranes.
This provides a potential explanation for the observed scatter of the C$_{60}$
band ratios. Our calculations suggest that a feature around 15$\mu$m due to the
breathing mode of heavily hydrogenated C$_{60}$ may be detectable
astronomically. A preliminary search for this feature in 35 C$_{60}$ sources is
reported.
