The purpose of this paper is to discuss the tests to detect an epidemic alternative in the mean value of a sequence of independent normal variables. Various test statistics, such as the likelihood ratio, the score-like statistic, Levin & Kline's statistic, the semilikelihood ratio, and the recursive residual, are studied. The large deviation approximations to the significance levels and powers are developed by integrating approximations to conditional boundary crossing probabilities. Some results of Monte Carlo experiments confirm the accuracy of these approximations. A numerical comparison of the different tests is made.