We present a biophysical model of a slowly inactivating potassium ion current IKS, based on recent voltage-clamp data from layer V pyramidal neurons in the cat sensorimotor cortex and show that the interplay between a persistent sodium current INaP and IKS is able to produce intrinsic membrane potential oscillations in the 10- to 50-frequency range. A most notable characteristic of such rhythmicity is what may be termed mixed-mode bursting, where clusters of action potentials alternate in time with epochs of small subthreshold oscillations.