The so-called dual-frequency nematic mixtures are very promising components for applications in fast operating devices. Compared with classical nematics, they exhibit positive or negative anisotropy of the electric permittivity depending on the applied frequencies of an external electric field. Owing to this property, an overall switching process from planar to homeotropic orientations, and vice versa, can be shortened by using the electric field with two different frequencies. Electro-optical switching characteristics of transmission versus time as a function of applied voltage were obtained for two different dual-frequency mixtures in twisted nematic cells. For one of the investigated mixtures, unusual decrease in the light transmission at switching from the homeotropic to planar orientation at threshold voltage was observed. The switching process apparently occurs in two steps. The mechanism of the two-step switching at twisted dual-frequency nematic structures was discussed. The explanation of the switching mechanism takes into account the influence of the electric field with different frequencies on molecules with transverse and longitudinal dipole moments. Moreover, molecular structure of compounds constituting the mixtures was analyzed. Additionally, response times of the switching driven with low and high frequency pulses were shown. This work helps to understand the molecular interaction and electro-optical switching in the dual-frequency nematic liquid crystals.