The excitation of the v(3) = 1 (sigma(g)+ C-C stretch) and the v(7) = 2 (pi(2)(g) C C-C bend) modes in the A(2)Pi(u) electronic state of diacetylene cations results in Renner-Teller (R-T) and Fermi interactions. The 3(0)(1) and 7(0)(2) vibronic bands in the A(2)Pi(u)-X-2 Pi(g) transition of HC4H+ have been measured with rotational resolution using cavity ringdown spectroscopy in a supersonic slit jet discharge. The analysis yields T-00 = 20520.828(4) cm(-1), B' = 0.14047(2) cm(-1), and A' = 17.95(1) cm(-1) for the v(3) = 1 and T-00 = 20573.659(4) cm(-1), B' = 0.14018(3) cm(-1), and A' = 11.55(1) cm(-1) for the v(7) = 2 level in the A(2)Pi(u) electronic state. A vibronic analysis has been carried out taking into consideration the R-T, spin-orbit, and Fermi resonance interactions between the v(3) and v(7) modes. The levels are fitted to the eigenvalues of an appropriate Hamiltonian matrix. This yields the vibrational frequencies omega(3)' = 811.8 cm(-1) and omega(7)' = 403.2 cm(-1), Renner parameter epsilon(7)' = 0.065, Fermi coefficients W-1' = 10.3 cm(-1) and W-2' = 5.1 cm(-1), and spin-orbit interaction constant A(SO)' = 31.1 cm(-1). A corresponding R-T analysis has been carried out for the X-2 Pi(g) ground state of HC4H+ using data available in the literature [Callomon, J. H. Can. J. Phys. 1956, 34, 1046]. This gives omega(3)'' = 956.2 cm(-1), omega(7)'' = 435.4 cm(-1), epsilon(7)'' = 0.028, W-1 '' = 7.2 cm(-1), W-2 '' = 10.9 cm(-1), and A(SO)'' = -33.3 cm(-1).