The IR-UV double resonance spectroscopy has been applied to observe the rovibronic level system of the ungerade nv(3)' + v(4)' and nv(3)' + v(6)'(n = 2, 3) vibrational states in the (A) over tilde (1)A(g)(S-1) state of acetylene which are accessible from the selected rotational level J " of the v(3)" state in the (X) over tilde (1)Sigma (+)(v) state. As was reported by Utz et al. [J. Chem. Phys. 1993, 98, 2742] for the v(4)' and v(6)' bands, the nv(3)' + v(4)' and nv(3)' + v(6)'(n = 2,3) states are found to couple with each other by the a- and b-axis Coriolis interactions. The rotational analysis is performed taking the Coriolis interactions into account to determine the spectroscopic constants including thr vibrational term values. The extent of the Coriolis interactions between nv(3)' + v(4)' and nv(3)' + v(6)'(n = 2,3) is not so significant as that between v(4)' and v(6)'. This is due to a larger anharmonic coupling of the in-plane trans-bending v(3)' mode with the in-plane cis-bending v(6)' mode than with the out-of-plane torsion v(4)' mode, which causes a larger energy spacing between the pairs of the interacting levels as the v(3)' quantum number increases. It is also found that most of rotational lines in the 3v(3)' + v(6)' band split into two or more peaks due to the S-1-T-3 interaction, while such rotational line splittings are not found in the 3v(3)' + v(4)' band. The present finding that the additional excitation in the out-of-plane torsion (v(4)') mode suppresses the splittings suggests that the S-1-T-3 mixing occurs at the planar C-2h, or C-2v geometry rather than at the nonplanar C-2 geometry which is distorted along the torsional coordinate from the planar geometry.