A wheel assembly position identifying apparatus configured to be mounted in a vehicle equipped with rotational position detecting sections, each of which is adapted to detect a rotational position of one of wheel assemblies, the apparatus comprising: Transmitters, each of which is provided in one of the wheel assemblies; and a receiver, which is provided in a body of the vehicle, wherein each transmitter includes a transmission section, which is configured to transmit signals to the receiver, an acceleration sensor, which is configured to rotate together with the corresponding wheel assembly and detect acceleration acting on the acceleration sensor, the wheel assembly position identifying apparatus being characterized in that each transmitter further includes a transmission-side control section, which is configured to cause the transmission section to transmit a constant position signal and a position detecting signal, wherein the constant position signal is transmitted at a constant position based on the acceleration detected by the acceleration sensor, and the position detecting signal is transmitted at a constant power, and the receiver includes a reception section, which is configured to receive the signals, and a reception-side control section, which is configured to execute a first identifying process and a second identifying process, wherein, in the first identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on variations of the rotational positions of the wheel assemblies at the time when the constant position signals are received, and in the second identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on the received signal strength indications (RSSIs). Transmitters, each of which is provided in one of the wheel assemblies; and a receiver, which is provided in a body of the vehicle, wherein each transmitter includes a transmission section, which is configured to transmit signals to the receiver, an acceleration sensor, which is configured to rotate together with the corresponding wheel assembly and detect acceleration acting on the acceleration sensor, the wheel assembly position identifying apparatus being characterized in that each transmitter further includes a transmission-side control section, which is configured to cause the transmission section to transmit a constant position signal and a position detecting signal, wherein the constant position signal is transmitted at a constant position based on the acceleration detected by the acceleration sensor, and the position detecting signal is transmitted at a constant power, and a transmission section, which is configured to transmit signals to the receiver, an acceleration sensor, which is configured to rotate together with the corresponding wheel assembly and detect acceleration acting on the acceleration sensor, the wheel assembly position identifying apparatus being characterized in that each transmitter further includes a transmission-side control section, which is configured to cause the transmission section to transmit a constant position signal and a position detecting signal, wherein the constant position signal is transmitted at a constant position based on the acceleration detected by the acceleration sensor, and the position detecting signal is transmitted at a constant power, and the receiver includes a reception section, which is configured to receive the signals, and a reception-side control section, which is configured to execute a first identifying process and a second identifying process, wherein, in the first identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on variations of the rotational positions of the wheel assemblies at the time when the constant position signals are received, and in the second identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on the received signal strength indications (RSSIs). a reception section, which is configured to receive the signals, and a reception-side control section, which is configured to execute a first identifying process and a second identifying process, wherein, in the first identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on variations of the rotational positions of the wheel assemblies at the time when the constant position signals are received, and in the second identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on the received signal strength indications (RSSIs).