The problems concerning the registration of late latency auditory responses to electric stimulation in the patients wearing cochlear implants are considered. The renewed interest to this class of evoked potentials is due to unexplained differences in the results of cochlear implantation in the patients with the similar audiological data, etiology, age and the history of deafness as well as cochlear implant surgery in children of first years of life and the extended possibilities for speech processor programming. It is maintained that the advantages of this method include the possibility to objectively evaluate the ability of brain to detect and discriminate between different stimulus characteristics, such as loudness differences, temporal changes or speech tokens. This method is of great clinical significance for the electrophysiological monitoring of brain plasticity and documentation of the clinical effectiveness of different rehabilitation methods. Based on our own experimental and clinical results and the literature data, we consider the application of different electrically evoked late latency potentials for the monitoring of the auditory pathway maturation dynamics during the electric stimulation as well for the estimation of the effectiveness of cochlear implantation. It is concluded that the longer duration of deafness and later age at implantation result in immature morphology and delayed peak latencies and that patients with shorter latencies and higher amplitudes have better speech perception. The use of different classes of electrically evoked responses of auditory cortex could provide the objective control of the effectiveness of the rehabilitative measured in the children following cochlear implantation.