Aims. Disk-averaged infrared spectra of Neptune between 1.8 and 13 μm, obtained by the AKARI infrared camera (IRC) in May 2007, have been analysed to (a) determine the globally-averaged stratospheric temperature structure; (b) derive the abundances of stratospheric hydrocarbons; and (c) detect fluorescent emission from CO at 4.7 μm. Methods. Mid-infrared spectra (SG1 and SG2 channels of AKARI/IRC), with spectral resolutions of 47 and 34 respectively, were modelled using a line-by-line radiative transfer code to determine the temperature structure between 1-1000 μbar and the abundances of CH 4 , CH 3 D and higher-order hydrocarbons. A full non-LTE radiative model was then used to determine the best fitting CO profile to reproduce the fluorescent emission observed at 4.7 μm in the NG channel (with a spectral resolution of 135). Results. The globally-averaged stratospheric temperature structure is quasi-isothermal between 1-1000 μbar, which suggests little variation in global stratospheric conditions since studies by the Infrared Space Observatory a decade earlier. The derived CH 4 mole fraction of (9.0 ± 3.0) × 10 −4 at 50 mbar, decreasing to (0.9 ± 0.3) × 10 −4 at 1 μbar, is larger than that expected if the tropopause at 56 K acts as an efficient cold trap, but consistent with the hypothesis that CH 4 leaking through the warm south polar tropopause (62-66 K) is globally redistributed by stratospheric motion. The ratio of D/H in CH 4 of 3.0 ± 1.0 × 10 −4 supports the conclusion that Neptune is enriched in deuterium relative to the other giant planets. We determine a mole fraction of ethane of (8.5 ± 2.1) × 10 −7 at 0.3 mbar, consistent with previous studies, and a mole fraction of ethylene of 5.0 +1.8 −2.1 × 10 −7 at 2.8 μbar. An emission peak at 4.7 μm is interpreted as a fluorescent emission of CO, and requires a vertical distribution with both external and internal sources of CO. Finally, comparisons to previous L-band studies indicate significant variability of Neptune's flux densities in the 3.5-4.1 μm range, related to changes in solar energy deposition.