Quantitative understanding of the dynamics of particular cell types when responding to complex, natural inputs, is an important prerequisite for understanding the operation of the cortical network. Different types of inhibitory neuron are connected by electrical synapses to nearby neurons of the same type, enabling the formation of synchronized assemblies of neurons with distinct dynamical behaviours. Under what conditions is spike timing in such cells determined by their intrinsic dynamics and when is it driven by the timing external input? In this paper, we have addressed this question using a systematic approach to characterizing the input-output relationships of three types of cortical interneurons (fast spiking (FS), low-threshold spiking (LTS) and non-pyramidal regular-spiking (NPRS) cells) in the rat somatosensory cortex, during fluctuating conductance input designed to mimic natural complex activity. We measured the shape of average conductance input trajectories preceding spikes, and fitted a two-component linear model of neuronal responses which included an autoregressive term from its own output. This clearly separated the contributions of stimulus and discharge history, in a cell-type dependent manner. Unlike LTS and NPRS cells, FS cells showed a remarkable switch in dynamics, from intrinsically-driven spike timing to input-fluctuation-controlled spike timing, with the addition of even a small amount of inhibitory conductance. Such a switch could play a pivotal role in the function of FS cells in organizing coherent gamma oscillations in the local cortical network. Using both pharmacological perturbations and modeling, we show how this property is a consequence of the particular complement of voltage-dependent conductances in these cells.