Abstarct: Independence and dependence properties of random variables play a basic role in statistics and probability‎. ‎In most situations‎, ‎the random variables are not independent‎. ‎Hence‎, ‎we should study and use the different measures of dependence between random variables‎. ‎In this thesis‎, ‎particularly‎, ‎we focus on negatively superadditive-dependence (NSD) structure and its applications‎. ‎Moment inequalities could be used in many applications of probability‎, ‎e.g‎. ‎finding lower or upper bounds for moments which their exact values are not known‎. ‎Two useful moment inequalities for NSD random variables are Rosenthal-type maximal and Kolmogorov-type exponential inequalities‎. ‎In this thesis‎, ‎by using the mentioned inequalities‎, ‎we re-introduce the complete convergence of arrays of row-wise NSD random variables and the complete consistency for the estimator of nonparametric regression model baxsed on NSD errors‎. ‎Then‎, ‎we examine the performance of theoretical results by a simulation study‎.