We have developed a method that incorporates the time-frequency characteristics of neural sources into magnetoencephalographic (MEG) source estimation. This method, referred to as the time-frequency multiple-signal-classification algorithm, allows the locations of neural sources to be estimated from any time-frequency region of interest. In this paper, we formulate the method based on the most general form of the quadratic time-frequency representations. We then apply it to two kinds of nonstationary MEG data: gamma-band (frequency range between 30-100 Hz) auditory activity data and spontaneous MEG data. Our method successfully detected the gamma-band source slightly medial to the N1m source location. The method was able to selectively localize sources for alpha-rhythm bursts at different locations. It also detected the mu-rhythm source from the alpha-rhythm-dominant MEG data that was measured with the subject's eyes closed. The results of these applications validate the effectiveness of the time-frequency MUSIC algorithm for selectively localizing sources having different time-frequency signatures.