Summary: We studied the nature of fluctuations around the phase transition of vehicular traffic by analyzing a time series of successive variations of velocity, obtained from single-vehicle data measured by an onboard apparatus. We found that the probability density function calculated from the time series of variation of velocity is transformed irreversibly in the critical region, where a Gaussian distribution changes into a Lévy stable symmetrical distribution. The power-law tail in the Lévy distribution indicated that the time series of velocity variation exhibits the nature of the critical fluctuations generally observed in phase transitions driven far from equilibrium. Furthermore, single-vehicle data enabled us to calculate the time evolution of the local flux-density relation, which suggested that the vehicular traffic system spontaneously approaches a delicate balance between metastable states and congested-flow states. The nature of fluctuations enables us to understand mechanisms behind the spontaneous decay of the metastable branch at the phase transition. The power-law tail in the probability density function suggests that dynamical processes of vehicular traffic in the critical region are related to a time-discrete stochastic process driven by random amplification with additive external noise.