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The attenuation coefficient of longitudinal ultrasonic waves in the nematic-isotropic phase transition regions of liquid crystals has been measured as a function of both temperature and frequency. A sharp maximum is observed in the attenuation coefficient at the phase transition temperature Tc. The temperature dependence of the velocity has also been measured at 2 MHz, and a sharp minimum is observed at Tc. The anomalous changes of the ultrasonic propagation properties in the nematic phase near Tc are analysed and discussed by a phenomenological treatment based on the Landau-Khalatonikov theory of critical slowing down. On the other hand, behaviors in the isotropic phase near Tc are discussed in terms of the theory proposed recently by Imura and Okano. It is concluded that the anomalies are associated with the nematic-isotropic phase transition which is of first order even though it is nearly of second order.