In this paper, we develop an analytical framework to measure the vulnerability of superpeer networks against attack. Two different kinds of attacks namely deterministic and degree dependent attack have been introduced here. We formally model the superpeer networks with the help of bimodal structure and different attacks with the help of graph dynamics. Our analysis shows that fraction of superpeers and their connectivity have profound impact upon the stability of the network. The results obtained from the theoretical analysis are validated through simulation. The agreement between the simulation results and theoretical predictions is almost perfect. Categories and Subject Descriptors: C.2.0 [General]: Security and protection General Terms: Measurement, Security.