The results of an ab initio study of the vibronic structure in the a(1)Delta(g) electronic state of C2H2++ and its deuterated species (C2D2++) are presented. They are generated employing a simple model that incorporates the minimal number of terms contributing to the Renner-Teller effect. The trans- and cis-bending potential curves at planar nuclear arrangements are obtained by means of large-scale configuration interaction calculations. The corresponding harmonic vibrational frequencies are 717 and 650 cm(-1) for C2H2++, and 549 and 477 cm(-1) in the case of C2D2++. It is found that the splitting of the potential surfaces is moderate at trans-distortions of linearity, while it is extremely small at cis-bending vibrations. The eigenvalues and eigenfunctions of the model Hamiltonian employed are obtained by means of a perturbative and a variational approach.