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The conditions guarantying consistency and asymptotic normality of Least-Square estimators as well as the consistency of the usual tests for linear hypotheses in multivariate linear models are shown to be valid whenever almost optimal experimental designs are used.

Berry Esseen type bounds for the distribution of the nonlinear least-squares estimator as well as of a certain statistic useful for testing a hypothesis on a subset of the parameter vector are derived.

In the linear model with tests for linear hypotheses on β are based on the normal distribution assumption. In this paper it is studied how much the distributions of the test-criterions differ from their distributions under normality when Yn is not normally distributed.

Usually the variance of independent observations resulting from a linear or a nonlinear relationship is estimated by the Least-Squares residual estimator. In this paper its asymptotic properties are investigated. Further the asymptotic behaviour of tests for one-sided hypotheses on the variance is studied. The paper splits into two parts, the first one concerned with linear and the second one with nonlinear models.