The vibronic splitting and Zeeman effect of ⁴A_2g to ²E_g* nu (t_1u) and ⁴A_2g to ²E_g* nu (t_2u) vibronic transitions are considered theoretically. It is shown that when the excited state has pure orbital doublet character the ²E_g* nu (t_1u) and ²E_g* nu (t_2u) vibronic multiplets each split into ²T_1u and ²T_2u vibronic levels and the Zeeman splitting of the vibronic levels equals that of the parent electronic state. When the excited state also contains some orbital triplet character through spin-orbit interaction a further splitting becomes possible, giving a total of four levels. In this case the Zeeman splitting will no longer equal that of the parent electronic state, but can be calculated by diagonalising four 3*3 energy matrices. The relative intensities of ⁴A_2g to ²E_g vibronic transitions are expressed in terms of two parameters. It is shown that, for the ²A_2g(t₂³) to ²E_g(t₂³) transitions within a d³ ion, one of these parameters will be small. In this case the relative magnitudes of both the intensity and vibronic interaction parameters can be estimated and the likely vibronic splitting pattern predicted.