The purpose of this study is to make an empirical evaluation of Multivariate Sequential Procedures for Testing Means as proposed by J. E. Jackson. This was done by simulated sampling from a multivariate normal population with known means, both when the variance-covariance matrix is assumed known (Sequential χ²-Test), and when it is assumed unknown (Sequential T² -Test). The results indicate the test procedure, either the Sequential χ²-Test or the Sequential T² -Test, lead to satisfactory decisions. The tests are conservative but the α and β errors are of an appropriate magnitude. The method (Bhate's Conjecture) used to approximate the Average Sample Number appears to give good estimates of the size of sample needed to obtain a decision. / Master of Science