Nonlinear methods of fractal analysis and recurrence quantification analysis are becoming more commonplace in the cognitive and behavioral sciences. These methods are illustrated here in a tutorial style using self-paced reading data. Self-paced reading was performed in which each spacebar press revealed a story word-by-word or else sentence-by-sentence. Participant readers were either Ph.D. candidates in English literature or undergraduates from an introductory psychology course and the same story was read by all, either one time only or reread another time on another occasion. The nonlinear analyses revealed crucial differences between the word unit and sentence unit conditions. Performance in the word unit condition was dominated by a task specific strategy, yielding data patterns more like those observed in tapping tasks. Nonlinear analyses of the sentence unit condition, however, discriminated between graduate and undergraduate readers, and first readings of the story from re-reading. From these analyses, the repeated reading of the same story reveals a kind of uber-fluency, in a manner of speaking, of the Ph.D. candidates in English literature, whose performance stayed at or closer to a performance ceiling in both readings.