A wheel assembly position identifying apparatus, which is mounted in a vehicle having rotational position detecting sections that detect, as detection values, rotational positions of respective wheel assemblies, wherein a transmitter is provided in each of the wheel assemblies, and the apparatus identifies in which of the wheel assemblies each transmitter is provided, the apparatus comprising: a receiver, which receives transmission signals that are each transmitted from one of the transmitters when the rotational position of the corresponding wheel assembly is a specific position; an obtaining section, which obtains the rotational position of each wheel assembly from the corresponding rotational position detecting section each time the receiver receives the transmission signal; a calculating section, which calculates a difference between the rotational position obtained by the obtaining section and a previously obtained rotational position; and an identifying section, which identifies the positions of the wheel assemblies, which are provided with the transmitters, by comparing the difference with a threshold, characterized in that: an accumulation threshold is employed as the threshold, the accumulation threshold being used to determine whether the received transmission signal has been transmitted at the specific position, and the identifying section determines whether an absolute value of the difference is greater than or equal to the accumulation threshold, accumulates the number of times the absolute value of the difference is determined to be greater than or equal to the accumulation threshold or the number of times the absolute value of the difference is determined to be less than the accumulation threshold, and identifies the positions of the wheel assemblies, in which the transmitters are provided, from an accumulated value obtained through the accumulation. a receiver, which receives transmission signals that are each transmitted from one of the transmitters when the rotational position of the corresponding wheel assembly is a specific position; an obtaining section, which obtains the rotational position of each wheel assembly from the corresponding rotational position detecting section each time the receiver receives the transmission signal; a calculating section, which calculates a difference between the rotational position obtained by the obtaining section and a previously obtained rotational position; and an identifying section, which identifies the positions of the wheel assemblies, which are provided with the transmitters, by comparing the difference with a threshold, characterized in that: an accumulation threshold is employed as the threshold, the accumulation threshold being used to determine whether the received transmission signal has been transmitted at the specific position, and the identifying section determines whether an absolute value of the difference is greater than or equal to the accumulation threshold, accumulates the number of times the absolute value of the difference is determined to be greater than or equal to the accumulation threshold or the number of times the absolute value of the difference is determined to be less than the accumulation threshold, and identifies the positions of the wheel assemblies, in which the transmitters are provided, from an accumulated value obtained through the accumulation. determines whether an absolute value of the difference is greater than or equal to the accumulation threshold, accumulates the number of times the absolute value of the difference is determined to be greater than or equal to the accumulation threshold or the number of times the absolute value of the difference is determined to be less than the accumulation threshold, and identifies the positions of the wheel assemblies, in which the transmitters are provided, from an accumulated value obtained through the accumulation.