A combined experimental and theoretical study of the energy loss of protons in fluorides and organic films is presented. The measurements were performed in fresh AlF3, LiF, and N,N′-bis(1-ethylpropyl)-perylene-3,4,9,10- tetracarboxdiimide (EP-PTCDI) evaporated in situ on self-supported C or Ag foils, covering the very low energy range from 25 keV down to 0.7 keV. The transmission method is used in combination with time-of-flight (TOF) spectrometry. In the case of fluorides with large band gap energies (AlF3 and LiF), the experimental stopping power increases almost linearly with the mean projectile velocity showing a velocity threshold at about 0.1 a.u. These features are well reproduced by a model based on quantum scattering theory that takes into account the velocity distribution and the excitation of the active 2p electrons in the F- anions, and the properties of the electronic bands of the insulators. In the case of the semiconductor organic film with a lower gap, the experimental stopping power increases linearly with the mean projectile velocity without presenting a clear threshold. This trend is also reproduced by the proposed model. © 2010 The American Physical Society.