The electronic structure and various molecular properties of the actinide (An) dicarbides ThC(2) and UC(2) were investigated by relativistic quantum chemical calculations. We probe five possible geometrical arrangements: two triangular structures including an acetylide (C(2)) moiety, as well as the linear AnCC, CAnC, and bent CAnC geometries. Our calculations at various levels of theory indicate that the triangular species are energetically more favorable, while the latter three arrangements proved to be higher-energy structures. Our SO-CASPT2 calculations give the ground-state molecular geometry for both ThC(2) and UC(2) as the symmetric (C(2v)) triangular structure. The similar and, also very close in energy, asymmetric (C(s)) triangular geometry belongs to a different electronic state. DFT and single-determinant ab initio methods failed to distinguish between these two similar electronic states demonstrating the power of multiconfiguration ab initio methods to deal with such subtle and delicate problems. We report detailed data on the electronic structure and bonding properties of the most relevant structures.