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Neural conduction delay is a serious issue for organisms that need to act in real time. Various forms of flash-lag effect (FLE) suggest that the nervous system may perform extrapolation to compensate for delay. For example, in motion FLE, the position of a moving object is perceived to be ahead of a brief flash when they are actually colocalized. However, the precise mechanism for extrapolation at a single-neuron level has not been fully investigated. Our hypothesis is that facilitating synapses, with their dynamic sensitivity to the rate of change in the input, can serve as a neural basis for extrapolation. To test this hypothesis, we constructed and tested models of facilitating dynamics. First, we derived a spiking neuron model of facilitating dynamics at a single-neuron level, and tested it in the luminance FLE domain. Second, the spiking neuron model was extended to include multiple neurons and spike-timing-dependent plasticity (STDP), and was tested with orientation FLE. The results showed a strong relationship between delay compensation, FLE, and facilitating synapses/STDP. The results are expected to shed new light on real time and predictive processing in the brain, at the single neuron level.