Lett1andt12be two independent normally distributed random variables with zero means and equal variances, each divided by a common estimate of the standard deviations. The joint distribution oft1,t2is a bivariate Studentt-distribution. The integral of the joint frequency function over certain types of critical regions in the (t1,t2)-plane may be written as the linear combination of two definite integrals which are easy to compute. Critical values for five alternative hypotheses in simultaneous tests ont1andt2are presented, and approximations which are asymptotically exact are discussed.