The microscopic origin of the VE coupling constant with the Jahn-Teller mode Eg for orbital triplet states corresponding to several excited states of MnF4+6 and the 4T2g state of CrF3−6 is explored by molecular orbital (MO) calculations. VE is shown to be determined by the splittings δe and δt induced in the antibonding emath image and tmath image levels by a Qθ(∼3z2− r2) distortion and so VE < 0 for the 4T2g state of CrF36 leading to a compressed octahedron as equilibrium geometry. VE values have been derived from self-consistent charge extended Hückel and MSXα calculations performed at different Qθ values. The results for the 4T1g(G), 4T2g(G), 4T2g(D), and 4T1g(P) states of MnF46 are reasonably close to the experimental figures. For the first excited state 4T1g(G) the value VE ∼ 60 cm−1/pm found for a metal-ligand distance R equal to 213 pm leads to a Huang-Rhys factor SE = 1.5 also close to experimental findings. On passing from this case to the 4T2g state of CrF36−[VE] increases by a factor of about two but SE =S 1.2 in agreement with experimental data for Rb2KGaF6: Cr3+. The latter figure implies a Stokes shift E0S(E) due to the Eg mode equal to 1200 cm−1 which is about 50% of the total Stokes shift. As a salient feature it is shown that for both MnF4−6 and CrF3−6 complexes VE strongly depends upon R, as it also happens to the VA coupling constant with the symmetric A1g mode. This reasonably explains the increase of the Stokes shift upon increasing R recently observed for Mn2+−doped fluoroperovskites. Although pure crystalfield (CF) theory gives rise to VE values much smaller than the experimental ones it is shown that, the relation VA/VE = equation image derivedforthe first excited state of MnF4−6 and CrF3−6 is no far from the results obtained through MO calculations.