This study investigates the dynamics of a human-driven vehicle (HV) following an automated vehicle (AV) when the latter performs a guidance of the former one. After performing linear stability analysis, the relevant nonlinearity in the range policy of the human driver is taken into account, and the string stability of the system is analysed for different excitation amplitudes of the reference velocity. The results show that applying small positive values for the cruise control gain is advisable, while the backward-looking gain should somewhat be increased when the nonlinear effects are relevant.