Four experiments are reported in which the materials are derived from two 12-tone serial compositions (Schoenberg's Wind Quintet and String Quartet, No. 4). Two experiments use the probe tone method (Krumhansl & Shepard, 1979) to assess factors contributing to tone prominence in serial music. The contexts in Experiment 1 are musically neutral statements of the complete or incomplete tone rows; the contexts in Experiment 4 are excerpts from the two pieces. Two experiments use a classification task to evaluate whether the prime form of the row is perceived as similar to its mirror forms (inversion, retrograde, and retrograde inversion). The materials are neutral presentations of the forms (Experiment 2) or excerpts from the pieces (Experiment 3). Large individual differences are found. A subgroup of listeners, with more music training on average, show the following effects in the probe tone experiments: low ratings for tones sounded more recently in the contexts and high ratings for tones not yet sounded; low ratings for tones fitting with local tonal implications; similar patterns for the neutral contexts and the musical excerpts. The remaining listeners show the opposite effects. Classification accuracy of mirror forms is above chance and is higher for the neutral sequences than the musical excerpts; performance is correlated with music training. The experiments show that some, but not all, listeners can perceive invariant structures in serial music despite mirror transformations, octave transpositions of tones, and variations of rhythm and phrasing.