Absolute photoionisation cross sections of Sr⁺ have been measured using merging beams of monochromatic (0.2< Delta lambda <1.0 AA) VUV synchrotron radiation (300< lambda <600 AA) and unexcited Sr⁺ ions. The absolute accuracy was assessed to be +or-15%. More than 30 peaks were identified in the photoionisation spectrum, the largest of which corresponded to a partially resolved doublet with energies of 26.95 and 26.97 eV and a total oscillator strength of 1.9. These energies are close to the term energy of 26.77 eV and doublet splitting of 0.02 eV calculated by Hansen (1975). There is also close agreement between these measurements of some autoionising energies of Sr⁺ and series limits in the photoionisation spectrum of neutral strontium (Mansfield and Newsom 1981) and with energies deduced from the spectrum of electrons ejected from strontium vapour by electron bombardment obtained by Schmitz et al. (1976) and White et al. (1979).