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Precise tests of Lorentz invariance can be executed using neutrinooscillations, which can provide sensitive measurements of suppressed signals ofnew physics. This talk describes the neutrino sector of the Standard-ModelExtension, which represents a general modification of the Standard Model ofmassive neutrinos to include Lorentz and CPT violation. Attainablesensitivities as well as a framework to search for these violations arepresented for existing and future long-baseline neutrino experiments. Theapplicability of this framework to short-baseline experiments is alsodiscussed.