Two experiments that investigate the perception of structural stability in atonal music are reported. The first experiment suggests that listeners may hear atonal music in terms of the relative structural importance of events and that listeners' hearing is greatly influenced by metrical and durational structure. A second experiment reveals that, even in the absence of clear rhythmic, timbral, dynamic, and motivic information, listeners infer relationships of relative structural stability between events at the musical surface. The effects of three main variables (pitch commonality, horizontal movement, and dissonance) and two salience criteria (register and parallelism) are considered. The results indicate that in the absence of a clearly differentiated surface structure, listeners' judgments of stability are influenced by the dissonance of chords and the horizontal movement of voices. It is concluded that salience (phenomenal accents), voice-leading, and dissonance are potentially important factors in the abstraction of relationships of relative structural importance, and hence to any inference of prolongational structure in atonal music.