The A3Πi–X3Σ− emission systems of OH+ and OD+ have been reinvestigated in detail. Fourteen bands have been analyzed (of which seven are new), and accurate rotational constants have been obtained for the levels ν = 0–2 in the two states of OH+ and ν = 0–3 in the two states of OD+. Corrected assignments are given for the low J lines in the bands of OH+ (which are important in astrophysical spectra, such as those of H2O containing comets).The perturbations in the A3Π states of both isotopes have been studied quantitatively, and the erratic Λ doubling explained in detail. The position of the perturbing b1Σ+ state has been determined to within a few cm−1, and minor perturbations by the A1Δ state have been characterized. Values of the spin–orbit coupling constant, A, and the spin–spin interaction parameter, α, have been extracted from the data for OD+A3Π ν = 0.