THE globular clusters NGC288 and NGC362 are central to recent claims 1-4 of large age differences (approximately 3 Gyr) between globular clusters associated with our Galaxy. According to standard models for the formation of the Galaxy 5, the system of globular clusters formed during the dynamical collapse of the protogalactic cloud, a process which should have lasted no more than 1 Gyr 6. But the claimed age differences are derived from stellar evolution models using assumed CNO abundances, and uncertainty in the actual CNO abundances of about a factor of three could account for an apparent 2-Gyr age difference 7,8. We have accurately measured abundances in red giants in NGC288 and NGC362, and find that the Fe abundance and the sum of the C, N and O abundances are essentially the same in every star studied. By eliminating compositional differences and thus confirming the reality of the age difference, these results imply a cluster formation period that is hard to reconcile with the standard collapse model 5,6.