In banking systems, there is a tendency for crises to spread from one institution to another. Such spread, if it occurs, can lead to a ‘systemic failure’, i.e. a large-scale crisis affecting the entire system. Systemic failure may arise because of inter-locking exposures, whether through equity, debt or participation in a common payments system, of financial institutions to each other. The failure of one institution can have ‘knock on’ effects on the balance sheet of other institutions, leading to a contagion of failures throughout the system. The inter-bank credit market is an important means through which commercial banks cover short-falls in liquidity. Typically, this market is based on short-term borrowing and lending. This kind of linkage can help make the banking system more efficient by re-allocating resources from banks that have idle cash reserves to those that have a pressing need for these reserves. Its effect on the stability of the banking system is less clear. While many studies have emphasized the ex post destabilizing implications of one bank’s failure, there is an ex ante sense in which inter-bank credit can play a stabilizing role. By borrowing from banks with surplus liquidity, banks which face a temporary shortfall can survive as a result of inter-bank credit. This represents risk-sharing and, in and of itself, must help keep down the incidence of failures in the system. Of course, in the event of one bank’s failure, an inter-bank credit system could very well exhibit the symptoms of contagion, but this risk has to be weighed against the ex ante role. In collaboration with S. Jafarey and Francisco Padilla we developed a model which allows us to study both ex ante and ex post aspects of inter-bank credit for the stability of the financial system. Each bank faces fluctuations in deposits and stochastic investment opportunities which mature with delay. This creates the risk of liquidity shortages. An interbank market lets participants pool this risk but also creates the potential for one bank’s crisis to propagate through the system. We study banking systems with homogeneous banks, as well as systems in which banks are heterogeneous. With homogeneous banks, an interbank market unambiguously stabilises the system. With heterogeneity, knock-on effects become possible but the stabilising role of interbank lending remains so that the interbank market can play an ambiguous role. We believe that a crucial ingredient in the emergence of contagion is the nature of the network of credit and debit relationships in the system. Reserach in random networks has in fact recently revealed that epidemic models are strongly affected by the connectivity patterns characterizing the population in which the infective agent spreads. In particular it has been shown that in scale-free networks the epidemic process does not possess any epidemic threshold below which the infection cannot produce a ma jor epidemic outbreak or an endemic state. This feature affect also the choice of immunization strategies. Contrary to standard models, it is found that scale-free networks do not acquire global immunity from ma jor epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. Successful immunization strategies can be developed only by taking advantage of the inhomogeneous connectivity properties of the scale-free connectivity patterns. We are investigating how these issue may play a role in our model, in particular in identifing appropriate immunization strategies that may reduce the risks of contagion in the banking system.