Absolute measurements have been made of cross sections for the single ionization of He⁺ ions by electrons with energies which ranged from threshold (54·4 ev) to 10 kev. The results are in good agreement with those of an earlier experiment by Dolder et al. (1961) which was confined to energies below 1 kev. Cross sections for the single ionization of Li⁺ have also been measured for electron energies between 3 and 25 kev. Comparison of these results with calculations (performed elsewhere) based on the Born and Bethe approximations shows that, for both ions, the former approximation gives results in excellent agreement with the experiments when the electron energies exceed twenty times threshold, whilst the Bethe approximation is only valid for energies greater than about 50 times threshold.