Abstarct: In general, the robustness of a statistical method can be defined as its insensitivity to mild departures from the basic assumptions. In other words, if the characteristics of a statistical method are not affected by a small deviation from the basic assumptions, the method is described as robust. Because outliers strongly influence classical estimates of regression coefficients in linear models, robust estimators such as M-estimators are suggested. The level and power of classical tests are also significantly reduced in the presence of suspicious data. For solving the problem, robust tests are introduced. To perform a robust test about regression parameters, the asymptotic distribution of test statistic is determined. The methods are evaluated baxsed on the reliability of the model estimators and power of tests. In addition to examining some basic features of negatively super-additive dependent random variables in this thesis, we study robust M-tests in linear models with negatively super-additive dependent errors under certain conditions. Using Monte Carlo simulation studies, we compare classic and robust methods baxsed on estimators' reliability and power of tests as well.