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.
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