In 1988, Jean Guillou composed Hyperion on a commission from the French oil company, Société Nationale Elf Aquitaine, to celebrate its discovery of oil. He developed this theme of fire using his imagination, European philosophical concepts, and various myths. As with Messiaen, rhythm becomes a significant element in Guillou's organ music to convey a heightened dramatic story of an exaltation of fire and to represent the fourth movement of "Agni-Ignis." For aspects of rhythmic structure, I developed new methodology to analyze rhythm in six sections of "Agni-Ignis." Guillou uses experimental rhythmic techniques such as rhythmic subdivision, cycling, rhythmic ostinato, durational contrast, and rhythmic crescendo to build the musical structure of the piece. Among them, the primary subdivision of 16th-note groups organizes throughout the piece as a cyclic theme to convey the powerful and vivid mood of fire. This rhythmic group creates many pitch patterns as thematic transformation to provide both rhythmic and harmonic complexities. The two types of rhythmic ostinato, which is variable and invariable type, juxtapose below the manual's skillful rhythm to provide variety and unity. The other notable features of rhythm appear at the border of each section, such as rhythmic crescendo, durational contrast, 32nd-note groupings, rest and fermata to build tension and relaxation. The rhetorical figure of pitch D, which is another "fire theme" in the pitch aspect dominates the core section which has a much slower rhythm with sustained notes. In general, Guillou has been influenced by his predecessors such as his teacher, Messiaen, and Stravinsky. However, he is uniquely suited to explore the limitless possibilities of the organ in a more secular and avant-garde style. The purpose of this study is to give the performer new insight to guide his or her performance.