Аннотация:The recent surge of optics of hyperbolic metamaterials (HMMs) has been fueled by their fascinating optical properties, one of the most intriguing being their strong optical nonlocality. In this work we demonstrate that in metal nanorod-based HMMs the nonlocality results in fast and slow light effects in the propagation of femtosecond laser pulses in close spectral vicinity of the HMM epsilon-near-zero regime. These effects are switchable via the angle of incidence and light wavelength. We elucidate that revealed dynamical phenomena stem from the zero-transmission points of HMM and related phase singularities caused by the destructive interference of the main optical wave and the additional wave mediated by the spatial dispersion of light in the HMMs.