Ultrasonic study over glass transition temperature was made on two fast-ion conducting glasses, (AgI)x(Ag4P2O7)1-x with x = 0.75 and 0.80, in the temperature range of room temperature to 200-degrees-C. Ultrasonic velocity dispersion and the attenuation peak suggest the presence of three different phases, rather than two, for the supercooled liquid of these glasses. They are tentatively assigned as the AgI-rich phase, the Ag4P2O7-rich phase, and the AgI-Ag4P2O7 mixed phase.