ABSTRACT Combining information from multiple sources is a fundamental operation performed by networks of neurons in the brain, whose general principles are still largely unknown. Experimental evidence suggests that combination of inputs in cortex relies on nonlinear summation. Such nonlinearities are thought to be fundamental to perform complex computations. However, these non-linearities contradict the balanced-state model, one of the most popular models of cortical dynamics, which predicts networks have a linear response. This linearity is obtained in the limit of very large recurrent coupling strength. We investigate the stationary response of networks of spiking neurons as a function of coupling strength. We show that, while a linear transfer function emerges at strong coupling, nonlinearities are prominent at finite coupling, both at response onset and close to saturation. We derive a general framework to classify nonlinear responses in these networks and discuss which of them can be captured by rate models. This framework could help to understand the observed diversity of non-linearities observed in cortical networks. AUTHOR SUMMARY Models of cortical networks are often studied in the strong coupling limit, where the so-called balanced state emerges. In this strong coupling limit, networks exhibit without fine tuning, a number of ubiquitous properties of cortex, such as the irregular nature of neuronal firing. However, it fails to account for nonlinear summation of inputs, since the strong coupling limit leads to a linear network transfer function. We show that, in networks of spiking neurons, nonlinearities at response-onset and saturation emerge at finite coupling. Critically, for realistic parameter values, both types of nonlinearities are observed at experimentally observed rates. Thus, we propose that these models could explain experimentally observed nonlinearities.