The 0(0)(0) bands of the A (2)Pi <-- X (2)Pi and A (2)Pi(g)<--X (2)Pi(u) transitions of cyanodiacetylene and dicyanoacetylene cations have been rotationally analyzed at Doppler-limited resolution using frequency modulation absorption spectroscopy. The ions were generated in a liquid-nitrogen cooled hollow cathode modulated discharge incorporated in a White cell. Analysis of the rotational structure yields molecular parameters of the cations in the two electronic states, confirming linear geometries. The inferred spin-orbit and rotational constants are discussed in terms of the electronic structure of the isoelectronic cations. The spectrum of dicyanoacetylene cation reveals Lambda-type doubling consistent with the presence of a nearby (2)Sigma(g)(+) state. The second order spin-orbit splitting of the A (2)Pi(g) state is analyzed to predict the existence of the (2)Sigma(g)(+) state below the A (2)Pi(g) state.