Using Hodgkin-Huxley and isolated subthalamic nucleus (STN) model neurons as examples, we show that electrical high-frequency stimulation (HFS) suppresses sustained neuronal spiking. The mechanism of suppression is explained on the basis of averaged equations derived from the original neuron equations in the limit of high frequencies. We show that for frequencies considerably greater than the reciprocal of the neuron's characteristic time scale, the result of action of HFS is defined by the ratio between the amplitude and the frequency of the stimulating signal. The effect of suppression emerges due to a stabilization of the neuron's resting state or due to a stabilization of a low-amplitude subthreshold oscillation of its membrane potential. Intriguingly, although we neglect synaptic dynamics, neural circuity as well as contribution of glial cells, the results obtained with the isolated high-frequency stimulated STN model neuron resemble the clinically observed relations between stimulation amplitude and stimulation frequency required to suppress Parkinsonian tremor.