This paper describes the use of the ASSR as a promising tool for the objective frequency-specific assessment of hearing thresholds in children. The stimulus generally used for ASSR recording (single amplitude-modulated carrier) only activates a small area on the basilar membrane. Therefore, the response amplitude is low. A stimulus with a broader frequency spectrum can be composed by adding several cosines whose frequency intervals comply with the desired stimulus repetition rate. Compensation for the traveling wave delay is also possible with a stimulus of this type, leading to a better synchronization of the neural response and consequently higher response amplitudes especially for low-frequency stimuli. The additional introduction of frequency offset, which minimizes the risks of detecting stimulus artefacts, enables the use of a q-sample test for the response detection, which is important particularly at the lowest frequencies. The results of investigations carried out on a large group of normal-hearing test subjects (N = 70) confirm the efficiency of this stimulus design. The new stimuli lead to significantly improved ASSRs with higher SNRs and thus higher detection rates and shorter detection times.