Three different modes of fluorine chemisorption at the surface of SWNTs have been unambiguously evidenced and their respective amounts quantified, using selective thermal desorption. The C-F bonds formed in this case seem to correspond to the three kinds of bonds previously identified in the different forms of graphite fluorides. The overall bonding scheme in a fluorotube relates to the fluorination temperature used and always consists of a mixture of several C-F bond types in different proportions, making one essential difference with fluorographites. Metastability or different fluorine locations might be at the origin of the phenomenon.