Alpha rhythms (9–11 Hz) are a dominant feature of EEG recordings, particularly over occipital cortex on cessation of a visual stimulation. Little is known about underlying neocortical mechanisms so here we constructed alpha rhythm models that follow cessation of cortical stimulation. The rhythm manifests following a period of gamma frequency activity in local V1 networks in layer 4. It associates with network level bias of excitatory synaptic activity in favour of NMDA- rather than AMPA-mediated signalling and reorganisation of synaptic inhibition in favour of fast GABAA receptor-mediated events. At the cellular level the alpha rhythm depended upon the generation of layer 4 pyramidal neuron dendritic bursting mediated primarily by PPDA-sensitive NR2C/D-containing NMDA receptors, which lack the magnesium-dependent open channel block. Subthreshold potassium conductances are also critical. The rhythm dynamically filters outputs from sensory relay neurons (stellate neurons in layer 4) such that they become temporally uncoupled from downstream population activity.