With biological cells exposed to ac electric fields below 100 kHz, external field is amplified in the cell membrane by a factor of several thousands (low-frequency plateau), while above 100 kHz, this amplification gradually decreases with frequency. Below 10 MHz, this situation is well described by the established first-order theory which treats the cytoplasm and the external medium as pure conductors. At higher frequencies, capacitive properties of the cytoplasm and the external medium become increasingly important and thus must be accounted for. This leads to a broader, second-order model, which is treated in detail in this paper. Unlike the first-order model, this model shows that above 10 MHz, the membrane field amplification stops decreasing and levels off again in the range of tens (high-frequency plateau). Existence of the high-frequency plateau could have an important impact on present theories of high-frequency electric fields effects on cells and their membranes.