The two lowest-lying (X and 2)(1)Sigma(+) states, the first (3)Sigma(+), (3)Pi, (1)Pi, (3)Delta, and (1)Delta excited states of the AgCl molecule have been studied through extensive complete active space SCF+averaged coupled pair functional calculations, using a 19-active-electron relativistic effective core potential (RECP) for Ag, a 7-active electron RECP for chlorine and large optimized Gaussian basis sets for both atoms. The 2 (1)Sigma(+) and (3)Sigma(+) excited states present shallow relative minima very near the equilibrium geometry of the ground state, while the lowest (3,1)Pi states were found to be totally repulsive in the internuclear range studied. The (3,1)Delta states present very shallow minima around 5.2 a.u. The calculated spectroscopic constants for the ground- and excited states are compared with the available experimental data and have been found in good agreement. Even though the (3)Pi state is repulsive, it lies very close in energy to the 2 (1)Sigma(+) one near the equilibrium geometry of the ground state; thus, a strong (3)Pi-2 (1)Sigma(+) mixture through the spin-orbit interaction is predicted to occur that will lead to the fine-structure B state responsible for the recently revised B<--X transitions in AgCl. The C-X transition observed at 43 500 cm(-1), appears now to arise from a higher-lying root of the (1)Sigma(+) or Pi manifolds, perhaps the third (1)Sigma(+) root, while the D-X system seems to arise from the (3)Delta<--(1)Sigma(+) transition around 49 000 cm(-1).