Brains can process sensory information from different modalities at astonishing speed; this is surprising as already the integration of inputs through the membrane causes a delayed response. Experiments reveal a possible explanation for the fast processing, showing that neurons can advance their output firing rate with respect to their input current, a concept which we refer to as prospective coding. The underlying mechanisms of prospective coding, however, are not completely understood. We propose a mechanistic explanation for neurons advancing their output on the level of single action potentials and instantaneous firing rates. We show that the spike generation mechanism can be the source for the prospective (advanced) or retrospective (delayed) response as shown for prospective firing in cortical-like neurons and retrospective firing in hippocampal-like neurons (b, orange). Further, we analyse the Hodgkin-Huxley dynamics to derive a reduced model to manipulate the timing of the neuron’s output by tuning three parameters. We further show that slow adaptation processes, such as spike-frequency adaptation or deactivating dendritic currents, can generate prospective firing for inputs that undergo slow temporal modulations. In general, we show that adaptation processes at different time scales can cause advanced neuronal responses to time-varying inputs that are modulated on the corresponding time scales. The results of this work contribute to the understanding of how fast processing (prospective coding) and short-term memory (retrospective coding) can be achieved in the brain on the level of single neurons and might guide further experiments. The insights are highly beneficial for biologically plausible learning algorithms used for temporal processing and their implementation on neuromorphic hardware.