The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu2+ in BaFCI, which consist of the 4f7(6P7/2,) → 4f7(8S7/2) and 4f65d → 4f7 transitions, and the 4f7-4f65d excitation spectrum of Ce3+ in YPO4. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f65d → 4f7 spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the δ-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.