Constraints from clock-comparison experiments on violations of Lorentz and
CPT symmetry are investigated in the context of a general Lorentz-violating
extension of the standard model. The experimental signals are shown to dep
end on the atomic and ionic species used as clocks. Certain experiments usu
ally regarded as establishing comparable bounds are in this context sensiti
ve to different types of Lorentz violation. Some considerations relevant to
possible future measurements are presented. All these experiments are pote
ntially sensitive to Lorentz-violating physics at the Planck scale. [S0556-
2821(99)01223-0].