The change in optical properties of GafChromic films depends not only on the absorbed dose, but also on the linear energy transfer (LET) of the ionizing radiation. The influence of LET on the film dose-response relationship is especially important when films are applied for dosimetry of energetic charged particles. In the present study, we examined the response of the unlaminated EBT3 and MD-V3 films to proton, deuterium and helium beams with energies in the range of several megaelectronvolts (MeV). Films were exposed to doses up to 200 Gy and a model based on the bimolecular chemical reaction was chosen to fit the measured film signals. The LET in the active layers of the films and the dose correction factors were computed with Monte Carlo software TRIM. Signal quenching, observed for all ion beams in comparison to x-rays, was investigated as a function of the LET in the range of 10-100 keV µm-1. The response of the films got weaker with increasing the LET and showed no dependence on the ion species. The LET effect was quantified by introducing a modified expression for the relative effectiveness (RE) by which a unique RE value is assigned to a single LET. The RE defined in that way decreased from about 90% for LET of 10 keV µm-1 to less than 50% for LET of 100 keV µm-1. Similar behavior was observed for EBT3 and MD-V3 film models.