Vibronic interactions in the two energetically lowest electronic states ((X) over tilde (2)Pi(g)-(A) over tilde (2)Pi(u)) of the diacetylene radical cation (C4H2 center dot+) are theoretically examined here. The spectroscopy of these two electronic states of C4H2 center dot+ has been a subject of considerable interest and measured in the laboratory by various groups. Inspired by numerous, experimental data, we attempt here a detailed investigation of vibronic interactions within and between the doubly degenerate 11 electronic states and their impact On the vibronic structure. of each state. A vibronic,coupling model is constructed in a diabatic electronic basis and with the aid of ab initio quantum chemistry calculations. The vibronic structures of the electronic states are calculated by time-independent and time-dependent quantum mechanical methods. The progression of vibrational modes in the vibronic band is identified, assigned, and compared with the literature data. The nonradiative internal conversion dynamics is also examined and discussed.