Asymptotic Expansions for General Statistical Models 0.1. The aim of the book Our Contributions to a General Asymptotic Statistical Theory (Springer Lecture Notes in Statistics Vol. 13 1982 called Vol. I in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained and heuristic procedures are suggested for the construction of test and estimator sequences attaining these bounds. In the present volume these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions 1 2 adding one term (of order n ) to the limit distribution. As in Vol. I the investigation is general in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent identically distributed observations. 2 Moreover it is special in the sense that its concern are regular models (i.e. families of probability measures and functionals which are subject to certain general conditions like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance it appears justifiable to exclude them at this stage of the investigation.