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Atomic properties involving the low-lying excited states in alkaline-earth-metal ions are of current interest in many different applications ranging from tests of physics beyond the standard model to astrophysics. We have used the relativistic coupled-cluster theory to perform accurate calculations of the lifetimes of the lowest excited and states in singly ionized calcium, strontium, and barium. The importance of electron correlation in these calculations is emphasized. Our results are compared with the available experimental and theoretical data.