Certain critical infrastructure networks show some interconnections, relations and interactions with other ones, most frequently when located and operating within particular areas. Failures arising within one critical infrastructure network, can then negatively impact not only on associated systems, societies and natural environment, but also on mutual critical infrastructure networks. Therefore, interdependent critical infrastructure networks can be determined as network of critical infrastructure networks (network of networks approach). The paper presents safety analysis of the network of critical infrastructure networks, taking into account interconnections, relations and interactions between particular ones. Critical infrastructures networks as multistate systems are considered, by distinguishing subsets of no-hazards safety states, and crisis situation states, and by analysing transitions between particular ones. Issues introduced in the article are based on the assumption that one key critical infrastructure network impacts on functioning of other critical infrastructure networks - can reduce their functionality and change level of their safety and inoperability, furthermore, other networks can impact each other, too. Safety characteristics of network of critical infrastructure networks: safety function, mean values and standard deviations of lifetimes in particular safety state subsets, are determined, taking into account interdependencies between particular networks. The results are related to various values of coefficients defining the significance of influence of interdependencies among networks.