The single neuron is the basic element of information processing in nervous systems. In this thesis several properties of the dynamics of the generation of spikes are investigated theoretically as well as experimentally. Phase oscillators of different complexity are introduced as models to predict the timing of spikes. The neuron's intensity-response curve is used as a basic parameter in these models to make them easily applicable to real neurons. As a second important aspect of the spiking dynamics, the neuron's phase-resetting curve is used to extend the models. The phase oscillators turn out to be a good approximation of the spiking behavior of a neuron as long as it is stimulated in its super-threshold regime. However, it is shown by comparison with conductance-based models that these models, as well as all other one-dimensional models including the common integrate-and-fire model, fail, if the neuron is stimulated with currents fluctuating around its threshold. Spike-frequency adaptation is a common feature of many neurons. For various ionic currents, as a possible reason for adaptation, a general phenomenological model for the firing rate of adapting neurons is derived from their biophysical properties. This model is defined by the neuron's intensity-response curves and an adaptation time-constant. By means of this model the high-pass properties of spike-frequency adaptation can be quantified. Also the role of adaptation in supression of background noise is discussed. Both the phase oscillators and the adaptation-model are tested on auditory receptor neurons of locusts and the AN1, a primary auditory interneuron of the cricket {Teleogryllus oceanicus}. In both cases the models are in good agreement with the experimental data. By means of the models it is shown that adaptation in the receptor neurons is caused by ionic currents of the spike generator while in the interneuron it is the input which is already adapting. In addition, the influence of spike-frequency adaptation on the recognition of courtship songs is analysed.