In this paper, a binaural sound source lateralization spiking neural network (NN) will be presented which is inspired by most recent neurophysiological studies on the role of certain nuclei in the superior olivary complex (SOC) and the inferior colliculus (IC). The binaural sound source lateralization neural network (BiSoLaNN) is a spiking NN based on neural mechanisms, utilizing complex neural models, and attempting to simulate certain parts of nuclei of the auditory system in detail. The BiSoLaNN utilizes both excitatory and inhibitory ipsilateral and contralateral influences arrayed in only one delay line originating in the contralateral side to achieve a sharp azimuthal localization. It will be shown that the proposed model can be used both for purposes of understanding the mechanisms of an NN of the auditory system and for sound source lateralization tasks in technical applications, e.g., its use with the Darmstadt robotic head (DRH).