The compositions of Steve Reich and György Ligeti both contain periodic rhythmic structures. Although periods are not usually easily perceived, the listener may perceive their combinations in a hierarchy of rhythmic structures. This document is an attempt to develop an analytical method that can account for this hierarchy in periodic music. I begin with an overview of the features of Reich's and Ligeti's music that contribute to the property of periodicity. I follow with a discussion of the music and writings of Olivier Messiaen as a precedent for the periodic structures in the music of Reich and Ligeti. I continue by consulting the writings of the Israeli musicologist Simha Arom and describing the usefulness of his ideas and terminology in the development of my method. I explain the working process and terminology of the analytical method, and then I apply it to Reich's Six Pianos and Ligeti's Désordre.