Two-dimensional photoelectron spectroscopy is performed for studying autoionization of acetylene in the Franck-Condon gap between the X(2) Pi(u) and A(2)A(g) states of C2H2+. The photoelectron spectrum in the photon energy range from 12.8 to 13.6 eV shows exclusive vibrational excitation of the symmetric C-H stretching mode nu(1) of C2H2+(X(2) Pi(u)), which results from autoionization of the valence state (3 sigma(g))(-1)(3 sigma(u))(1). Vibrational frequencies with anharmonicities of the nu(1) and nu(2) (the symmetric C-C stretch) modes are determined by a least-squares fit of the ionization energies of the observed peaks to a second order expansion. At the photon energy of 14.120 eV, autoionization of the Rydberg state (3 sigma(g))(-1)(3p pi(u))(1) leads to a complicated photoelectron spectrum where probably the trans-bending mode nu(4) of C2H2+ (X(2) Pi(u)) as well as nu(1) is excited, reflecting a substantial metrical change during autoionization. Furthermore, a similar excitation of the nu(4) mode is observed at similar to 13.8 eV. An excellent agreement in positions of the vibrational levels between the spectra at 13.821 and 14.120 eV suggests the presence of the Rydberg stare (3 sigma(g))(-1)(3p sigma(u))(1) at similar to 13.8 eV which has not been identified previously in the photoabsorption or photoionization cross section curves. The constant-ionic-state spectra for the nu(1) = 0-4 levels of C2H2+ (X(2) Pi(u)) show two spectral features : (a) a weak shoulder (upsilon(1) = 0) or a small maximum (nu(1) = 1-4) at 13.8 eV and (b) two groups of peaks in the range of 14.0-14.4 eV. The ratio of the integrated intensity of the 13.8 eV maximum to that of the two groups differs from level to level. This observation is interpreted in terms of a strong interaction between the Rydberg (3 sigma(g))(-1)(3p sigma(u))(1) and valence (3 sigma(g))(-1)(3 sigma(u))(1) states.