Loss of the functionality, component and/or structure damage caused by insufficiency and failure of the material is usually called as limit state. There is a deformation history preceding to limit state, and, as a result, except for loss of machine functionality a material failure is taking place. The course is taken as a free continuation of the basic course on Limit States of Materials. It is focused on topics like deformation, fracture initiation and propagation under different loading conditons. There are traditional approaches to deformation and fracture behaviour evaluation included, e.g. plastic deformation at uniaxial loading, fatigue, creep, but, at the same time, up to date methods, used e.g. by low cycle fatigue and in particular by fracture mechanics. The phenomena are explained linking up to typical structural materials groups; the lectures are therefore especially suitable for the branches having less time or no dotation of courses oriented on materials.