Focal-ratio degradation (FRD) of light launched into high-numerical aperture (NA) single-annulus all-silica undoped air-clad fibres at an NA of 0.54 is reported. The measured annular light distribution remained Gaussian after 30 m of propagation, but the angular FWHM of the output annulus doubled from 4 • after 1 m propagation to 8.5 • after 30 m, which is significantly larger than that reported of standard doped-silica fibres (NA < 0.22). No significant diffractive effects were observed. The design of air-clad fibres for broad-band, high-NA astrophotonics applications is discussed.