Lett* denote an unknown abscissa of intersection of two true regression functions μ1(t) and μ2(t). Under normality assumptions with no restraints ont* the maximum likelihood estimator oft* is shown to be the corresponding intersection of the sample regressions. When this estimate exists confidence intervalsJcan usually be obtained fort* by an application of the Studentt-distribution. Whent* is restrained to some known intervalI, the ML estimate may or may not fall inI. A restrained ML estimate proposed is the limiting point of ∩I ∩Jas the length ofI ∩ Japproaches zero. Confidence limits are obtained for the restrained estimate. Many practical difficulties are discussed.