Neostriatal neurons may undergo events of spontaneous synchronization as those observed in recurrent networks of excitatory neurons, even when cortical afferents are transected. It is necessary to explain these events because the neostriatum is a recurrent network of inhibitory neurons. Synchronization of neuronal activity may be caused by plateau-like depolarizations. Plateau-like orthodromic depolarizations that resemble up-states in medium spiny neostriatal neurons (MSNs) may be induced by a single corticostriatal suprathreshold stimulus. Slow synaptic depolarizations may last hundreds of milliseconds, decay slower than the monosynaptic glutamatergic synaptic potentials that induce them, and sustain repetitive firing. Because inhibitory inputs impinging onto MSNs have a reversal potential above the resting membrane potential but below the threshold for firing, they conform a type of "shunting inhibition". This work asks if shunting GABAergic inputs onto MSNs arrive asynchronously enough as to help in sustaining the plateau-like corticostriatal response after a single cortical stimulus. This may help to begin explaining autonomous processing in the striatal micro-circuitry in the presence of a tonic excitatory drive and independently of spatio-temporally organized inputs. It is shown here that besides synaptic currents from AMPA/KA- and NMDA-receptors, as well as L-type intrinsic Ca(2+)- currents, inhibitory synapses help in maintaining the slow depolarization, although they accomplish the role of depressing firing at the beginning of the response. We then used a NEURON model of spiny cells to show that inhibitory synapses arriving asynchronously on the dendrites can help to simulate a plateau potential similar to that observed experimentally.