Abstract: It is well-known that, obtaining the necessary and sufficient conditions is not an easy task in the approximation theory. Necessary and sufficient conditions for the uniform approximation of a continuous function on a closed interval by positive linear operators are independently obtained by H. Bohman and P.P. Korovkin. These theorems are known as Bohman-Korovkin type, especially Korovkin type, theorems in the literature. Obtaining the direct and inverse results for positive linear operators is also important in this theory. The first inverse results for the Bernstein polynomials were given by G.G. Lorentz. And then many authors interested in these type researches. Some direct and inverse results for Gadjiev, Ibragimov operators have been obtained by A. Alt?n and O. Dogru in the previous WSEAS International conference on Applied Mathematics 2004. In a recent paper, necessary and sufficient conditions to obtain direct and inverse results for a sequence of general positive linear operators are given by O. Dogru. These results are valid for not only uniform approximation but also statistical approximation. The concept of statistical convergence was defined by H. Fast. Recently, a useful Korovkin type theorem for statistical convergence is proved by A.D. Gadjiev and C. Orhan. The importance of statistical convergence is that any convergent sequence is statistical convergent but not conversely. On the other hand, Voronovskaja obtained an asymptotic formula for the rate of convergence of Bernstein polynomials. Several studies showed that other many positive linear operators such as Meyer-Konig and Zeller operators, Bleimann, Butzer and Hahn operators, Lupas operators, Muller's Gamma operators, Kirov operators and their Kantorovich and Durrmeyer type integral generalizations have some asymptotic approximations. The main purpose of this talk is to give necessary conditions to obtain a Voronovskaja type asymptotic formula for a sequence of general positive linear operators via statistical limit.