The vulnerability analysis of our societies to major disturbances is of outmost importance in the fields of Infrastructure Asset Management (IAM). Several methodologies have already been developed to assess the vulnerability of critical infrastructures (CIs). Supply networks (water, gas, energy…) are also critical infrastructures (called Critical Networks or CNs hereafter), and should be considered with specific care due to (a) their complexity and spatial extent, (b) their role in providing other CIs with resources. In a first part, we present our framework for vulnerability and resilience in the French-German project “ResiWater” (Innovative Secure sensor Networks and Model-based Assessment Tools for Increased Resilience of water Infrastructures), funded by ANR and BMBF. We will then illustrate the various approaches to vulnerabilities. Lastly, we will draw our conclusions, which will be the guidelines for our project.