The effects of a global inhibition are studied on different models of neural networks, from the Wilson-Cowan model to networks of leaky integrate-and-fire neurons. These systems typically display a region of parameter space where two different states are possible, one of low and another of high activity with a phenomenology typical of first order phase transitions, with e.g. hysteresis in correspondence of a sweep of a control parameter. The introduction of a global inhibition, given by the presence of inhibitory interneurons with very large in-degree and out-degree, leads to a smoothing of the transition, accompanied by a marked increase of the fluctuations of the activity, that can be interpreted as a transformation of the first order transition into a second order one, and then into a phase without discontinuities. The biological relevance of the work is discussed, for example as a tool used by the brain to switch between the persistence of dynamical states, important for memory persistance or task performance, and the flexibility and dynamical range needed to respond in an effective way to a large number of external inputs.