An apparatus for detecting a decrease in a tire air pressure includes: a rotation velocity information detection means for periodically detecting tire rotation velocity information for the respective wheels of a vehicle; a frequency characteristic estimate means for estimating, based on this rotation velocity information, a frequency characteristic of the rotation velocity information; and a judgment means for judging, based on the estimated frequency characteristic, a decrease in the air pressure of the tire. The frequency characteristic estimate means includes, with regard to a time-series signal including the rotation velocity information, a parameter estimate means for subjecting parameters of a three-order or more linear model to a time-series estimate; an input signal estimate means for estimating, based on the estimated linear model and the rotation velocity information that is an output signal of the linear model, an input signal to the linear model; a parameter identification means for identifying, based on the estimated input signal and the rotation velocity information, parameters of a linear model caused to have a lower order of a second order; and a resonant frequency estimate means for estimating, based on the parameters identified based on the model caused to have a lower order of the second order, a resonant frequency of the tire in a torsional direction.