The lowest Omega=0(-),0(+),1,2 fine-structure potential energy curves arising from the two lowest-lying singlet (X (1)Sigma(+) and 2 (1)Sigma(+)) and the first (3)Pi electronic states of AgI were obtained through an effective Hamiltonian; the purely electronic LambdaSSigma energies were used as diagonal elements, which were calculated through extensive complete active space self-consistent field+averaged coupled pair functional calculations, with relativistic effective core potentials and optimized Gaussian basis sets for both atoms. The spin-orbit interactions were included using the Stuttgart effective spin-orbit potentials. For the excited Omega=0(+) states, very strong mixtures were found of the 2 (1)Sigma(+) and (3)Pi parents that lead to the fine-structure (0(+)) single B state (dominated by the 2 (1)Sigma(+) parent at long distance), that explains the B<--X transitions. The present results also explain the presence of a second long-distance minimum for the B0(+) state, experimentally Rydberg-Klein-Rees fitted. These calculations produced, as a byproduct, a new lower-lying Omega=0(+) yet unobserved fine-structure state predicted to exist around 22 000 cm(-1). Our theoretical results are compared and discussed in the light of the experimental data for the B-X transitions in silver halides [J. Chem. Phys. 109, 9831 (1998)]. (C) 2004 American Institute of Physics.