 To investigate the functional role of the cortical tracking of a background speech, we employed a simplified version of a coaxial party with two voices, the male and the female one. 18 participants were instructed to listen to a target voice and to ignore the distractor one while their auditory courtesans were stimulated with alternating current. The current waveforms were derived from the theta frequency portion of the speech envelope of either target or distractor voice. We determined the modulation of a speech comprehension through TACS by shifting the current waveforms by four different phases. We found that TACS with the target envelope resulted in a significant modulation of a speech comprehension such that the highest comprehension is for his observer at the zero phase shift and the lowest at the phase shift of about 180. TACS with the distractor envelope led to a significant modulation as well, also with a different phase dependence. The highest score occurred at the phase shift of 180 and the lowest at the phase shift of zero. We also found that the modulation caused by TACS with the target envelope is stronger than that of the distractor envelope. This stronger modulation may point to an effect of TACS with the target envelope that goes beyond auditory estimation, such as by adding the parsing of the speech stream into syllables and words. After aligning the phase relative to the best phase per subject, we found no significant modulation neither for TACS with the target envelope nor for TACS with the distractor envelope. Moreover, the distributions of the best phases of different subjects were significantly different from a uniform distribution for both types of neural stimulation, suggesting a consistent phase dependency across subjects.