### Abstract

Many questions which we can answer in the case of superstable groups remain open for stable not superstable groups: existence of an infinite definable abelian subgorup, link between definable simplicity and simplicity for example. Separably closed fields are a good place to test all these questions. In the case of definably simple groups, one is led rapidly to interesting questions about the classification of pseudo-reductive algebraic groups over separably closed fields (in the terminology of Tits).