Structure of Layered Double Hydroxides and the reaction occurring during thermal treatments are investigated. The reaction is supposed to be a grafting reaction of interlamellar species onto layers but its mechanism is not well known. These materials display a very poor level of organisation and the study of their fine structure involves the use of techniques sensitive to the local environments. XANES and EXAFS studies give few information about the grafting process because of the great disorder in the interlayer space. Much more information about the layers local structure are reached, revealing that distorted and regular octahedra coexist which is particular to layers containing copper atoms. It probably creates a local segregation undetectable by X ray diffraction study in anyway. It also highlights the difference of sheet thermal stability in function of the nature of the intercalated anion.