A theory of structural vulnerability is developed, in two linked papers, initially for two dimensional frame structures. The purpose of the theory is to enable the identification of the most vulnerable parts of a structural system so that they may be suitably protected and monitored. In Part 1 a graph model was used to analyse various load paths and loops within a structure based on the new concept of a structural ring. In this paper a deterioration hierarchy of structural rings shows all possible ways in which a structural ring can deteriorate into a mechanism. A failure scenario is described in terms of deteriorating events and a measure of the effort required, the damage demand, introduced. Three particular types of failure scenario are discussed and related to the concept of robustness.