Approximate problems that scalarize and approximate a given multiobjective optimization problem (MOP) became an important and interesting area of research, given that, in general, are simpler and have weaker existence requirements than the original problem. Recently, necessary conditions for approximation of several types of efficiency for MOPs have been obtained through the use of an alternative theorem. In this paper, we use these results in order to extend them to sufficient conditions for approximate quasi (weak, proper) efficiency. For this, we use two scalarization techniques of Tchebycheff type. All the provided results are established without convexity assumptions.