Numerical contributions to the asymptotic theory of robustness In the framework of this dissertation a software package the R bundle RobASt by means of the statistics software R has been developed. It includes all robust procedures introduced throughout the thesis. The dissertation itself consists of five parts and starts with a brief motivation which makes precise why robust statistics is necessary. After that a detailed summary in German and English is given. Part I provides a description of the asymptotic theory of robustness (Chapter 1) which forms the basis of this thesis. It is based on Chapters 4 and 5 of Rieder (1994). Chapter 2 provides supplements to the asymptotic theory of robustness which have proved necessary for this thesis. More precisely it contains results about: properties of the optimally robust influence curves (ICs) how one should proceed in an optimal way if the neighborhood radius is unknown as mostly in practice and the construction of estimates by means of the one step method. At the end of Chapter 2 convergence of robust models is introduced which is related to the concept of convergence of experiments of Le Cam. Part II deals with optimally robust estimators for some non standard models in robust statistics. These models are covered by the R package ROptEst which makes use of S4 classes and methods and is part of the R bundle RobASt. More precisely the binomial (Chapter 3) and Poisson (Chapter 4) model the exponential scale and Gumbel location model (Chapter 5) as well as the Gamma model (Chapter 6) are investigated...