Longitudinal impedance and transversal admittance of overhead transmission line (OHTL) are dependent on the ground which the line conductors are located. Several models in the literature consider the soil as an ideal conductor which the resistivity ρ and relative permittivity εr are constants. However, frequency-dependent soils are characterized by frequency-dependent (FD) electrical parameters (ρ(f) and εr(f)) which different formulations to represent the soil with constant and FD parameters have been developed. In order to obtain a precise transient response, these formulations must be included to compute the ground-return impedance and admittance of a OHTL. In this article, soils of low and high resistivities are studied considering the constant and FD soil models. Simulations are carried out in a high frequency range for soil parameters (resistivity and relative permittivity), ground-return impedance, attenuation constant and phase velocity. Then, the transient voltages are calculated for OHTLs located above real and constant parameter soils generated by two types of disturbances: an energization maneuver and a lightning direct strike. The numerical results show significant differences between the responses obtained with the constant and FD soil models, which these variations are more pronounced for soils of high resistivity and for a short OHTL.