Simultaneous test procedures (STPS for short) in the context of the unrestricted full rank general linear multivariate model for population cell means are introduced and utilized to analyze interactions in factorial designs. By appropriate choice of an implying hypothesis, it is shown how to test overall main effects, interactions, simple main, simple simple main and simple interaction effects. Implicit in the STP procedure is the control of the type I error rate for an implied family of tests. A set of simultaneous confidence bounds around contrasts of population cell means can be constructed without increasing the type I error rate. Numerical examples are given to illustrate the method. (Author)