Multiconfigurational self-consistent field–multireference configuration interaction calculations followed by the inclusion of spin–orbit corrections were performed to study the 18 lowest (Ω) fine structure states arising from the 9 lowest purely electronic ΛSΣ states of the CuI molecule. An important difference with previous studies on the first excited states of CuF and CuCl is found regarding the relative position of the first neutral states [with the Cu(d10s1)I(s2p2σp3π) configuration] even before taking into account the spin–orbit effects. We have been able to assess the nature of the observed transitions and verified that the first (A) and third (D) systems arise both from a Σ←Π-type transition while the second (C) and fourth (E) systems arise from a Σ←Σ type. The adiabatic potential energy curves for all the Ω states are given as well as the calculated spectroscopic constants of the states having a minimum in the studied range of interatomic distance. We also confirm the hypothesis put forward by Delaval et al.[Chem. Phys. Lett. 139, 212 (1987)] stating that the X←A and X←C transitions are spin forbidden. We explain this through the mixing of singlet and triplet states owing to the spin–orbit coupling of iodine (for the A 1,3Πn state) and that due to copper (for the C 3,1Σ+ state). Finally, an avoided crossing is predicted between the third and fourth Ω=1 fine structure states and a dramatic change of character for the D(1Π) ionic state towards a neutral Π configuration at long interatomic distance.