In case of nutritional stress, Escherichia coli cells abandon their exponentially-growing state to enter a more resistant, non- or slow-growing state termed stationary phase. This growth-phase transition is controlled by a genetic regulatory network integrating various environmental signals. Although E. coli is a paradigm of the bacterial world, it is not known how its adaptative response to nutritional conditions emerges from the interactions between the different components of the genetic network. Moreover little quantitative data on kinetic parameters and molecular concentrations are available. To overcome these constraints, we use a qualitative simulation method to model the nutritional stress response network and to simulate the response of E. coli cells to nutrient deprivation. Using this method, we are able to capture essential features of the transition between exponential and stationary phase and to make new predictions concerning the system behavior, that are currently under experimental validation.