The intramolecular vibrational energy redistribution (IVR) of acetylene in the electronically ground state is analyzed by a novel method called derivative state analysis [K. Someda, Bull. Chem. Soc. Jpn. 69, 3037 (1996)]. The derivative state analysis clarifies how the Hilbert space of quantum states are explored in IVR, and we are thereby able to classify the quantum states and to know their genealogy. The Hamiltonian presented by Temsamani and Herman [M. A. Temsamani and M. Herman, J. Chem. Phys. 102, 6371 (1995)] is adopted in the analysis. The IVR from three different types of initial vibrational states are analyzed: (1) The initial states excited in the trans-bending (nu(4)) mode undergo a rapid and instantaneous IVR when upsilon(4) greater than or equal to 10. (2) The IVR from the states with the CH antisymmetric stretch (nu(3)) excitation has an onset at nu(3) = 6 and is sequential. The vibrational energy is transmitted from the nu(3) mode to the CC stretch (nu(2)) in the first stage and then to the trans- and cis-bending. (3) Simultaneous excitation in nu(2) and nu(4) modes also gives rise to sequential IVR, in which the energy flows via cis-bending (nu(5)) to symmetric CH stretch (nu(1)) and nu(2).