By coupling a head-tracking system with a binaural rendering, the latter becomes dynamic. This allows coherence between the orientation of a listener’s head and the virtual sound scene. Nevertheless, the head-tracking data has to be transmitted to the audio rendering, which must then compute the orientation of a new virtual audio scene. In this way, a latency between the head movement and the audio rendering is unavoidable. If this latency is too high, a feeling of elasticity, or even spatial incoherence, is felt, which is detrimental to the listening experience. In this study, a perceptual test was conducted in order to investigate the influence of HRIRs on a latency detection threshold task, using an adaptive procedure. The subjects listened to two excerpts (a male voice and a pink noise) with their own HRIRs or with non-individual HRIRs. Two head movements in azimuth, with different rotation speeds, were imposed. Results showed significant differences between slow and fast movements and between the pink noise and the male voice. No global difference was observed between non-individual and individual HRIRs.