The importance of measuring electron-ion excitation cross sections in singly and multiply charged positive ions is outlined, and recent results for Mg II and O II ions are given using the Jet Propulsion Laboratory's electron energy-loss mereged-beams apparatus. For Mg II, collision strengths are presented for the 3s 2S→3P(h, k) resonance transition at electron energies from threshold to approximately 9¿ threshold (40 eV). Theoretical comparisons are also given with two five-state close-coupling calculations. The energy variation of the collision strength is fitted with a semiempirical analytic function which includes approximations to polarization, resonance, and exchange contributions. In O II, first spectra anywhere of electron excitation of the optically allowed 2s22p3 4S0→ 2s2p4 4P(14.88 eV) and →2p23s 4P(22.98 eV) transitions are presented. In addition, excitations of the two low lying, optically forbidden transitions 4S0→2p3 2D0 (3.33 eV) and →2p3 2P0 (5.02 eV) are detected for the first time.