The T(16O,p)18O reaction has been employed to measure the lifetimes of the 1.98 MeV 2+ level (τ = 3.35 ± 0.20 ps) and the 3.55 MeV 4+ level (τ = 24.5 ± 3.3 ps) of 18O by the recoil distance method. The lifetime of the 1.89 MeV 2+ level of 18Ne (τ = 0.63 ± 0.13 ps) has been measured by observing the Doppler shift attenuation of γ rays from 18Ne ions recoiling from the 16O(3He,n) reaction into Y and Ta backings. Transition rates in these mirror nuclei are compared with theoretical predictions.