The infrared spectra, as well as the integrated molar absorptivity (Ψ) and the molar extinction coefficient (ɛ) of each infrared transition of the hydrogenated fullerenes (known as fulleranes) C60H36, C60H18 and C70H38, and a mixture of fulleranes generally referred to as 77 per cent of C60Hx and 22 per cent C70Hy with x≈y > 30, are presented and discussed. These data are useful for the search, identification and quantitative determination of fulleranes in space after the recent discovery that their parent molecules, C60 and C70, are more abundant in space than initially thought, being present in a variety of H-rich circumstellar environments such as planetary nebulae and only mild H-deficient R Coronae Borealis stars, and in the interstellar medium. It is shown that the C-H stretching band of the fulleranes C60H36, C60H18 and C70H38, and their mixture may be most useful for the identification of these molecules because their Ψ and ɛ values are unique in terms of strength, overcoming by far the typical Ψ and ɛ values of reference molecules such as adamantane and docosane, as well as typical ɛ literature data for aliphatic molecules. In contrast to the rather simple infrared spectra of C60H36 and C60H38, the infrared spectra of two C60H18 isomers are reported as characterized by a rich number of bands which may allow an easier identification than the higher homologues. The dependence of the infrared bands of fulleranes on temperature was studied over a wide range of temperatures (from -180°C to +250°C) and extrapolated to 0 K.