We used whole‐cell recordings to investigate subthreshold membrane potential oscillations and their relationship with intermittent firing in striatal fast‐spiking interneurons. During current injections (100–500 pA, 1 s), these cells displayed a highly variable pattern of spike bursts (comprising 1–30 action potentials) interspersed with membrane potential oscillations. The oscillation threshold was −42 ± 10 mV, and coincided with that for action potentials. The oscillation frequency was voltage dependent and ranged between 20 and 100 Hz. Oscillations were unaffected by the calcium channel blockers cadmium and nickel and by blockers of ionotropic glutamate and GABA receptors. Conversely, the sodium channel blocker tetrodotoxin fully abolished the oscillations and the spike bursts. The first spike of a burst appeared to be triggered by an oscillation, since the timing and rate of rise of the membrane potential in the subthreshold voltage region was similar for the two events. Conversely, the second spike (and the subsequent ones) displayed much faster depolarisations in the subthreshold voltage range, indicating that they were generated by a different mechanism. Consistent with these notions, a small pulse of intracellular current delivered during the oscillation was effective in triggering a burst of action potentials that largely outlasted the pulse. We conclude that fast‐spiking interneuron oscillations are generated by an intrinsic membrane mechanism that does not require fast synaptic transmission, and which depends on sodium conductance but not calcium conductance, and that such oscillations are responsible for triggering the intermittent spike bursts that are typical of these neurons.