Surface and internal charging of dielectric materials is a potential cause of surface discharges and satellite anomalies, due to the fluctuating irradiation levels induced by space environment. Understanding conduction mechanisms and reducing charging levels are therefore important industrial issues for satellite designers and manufacturers. Surface potential measurements under irradiation and after charging (potential decay) are the most significant laboratory tests to qualify and understand the charging and discharging behavior of insulating materials. We present here experimental results obtained using the SIRENE facility at ONERA. Kapton and Teflon FEP films respond differently when subjected to a 20 keV charging electron beam combined with a 400keV ionizing electron beam. The physics underlying these experimental results is discussed. A simple numerical model has been developed. It is shown that different combinations of mobility, trapping and recombination may explain the results on both materials. The complex behavior observed on Teflon FEP may be attributed to the progressive deep trapping of the negative charge, enhancing holes recombination.