Behavioral rhythms synchronize between humans for communication; however, the relationship of brain rhythm synchronization during speech rhythm synchronization between individuals remains unclear. Here, we conducted alternating speech tasks in which two subjects alternately pronounced letters of the alphabet during hyperscanning electroencephalography. Twenty pairs of subjects performed the task before and after each subject individually performed the task with a machine that pronounced letters at almost constant intervals. Speech rhythms were more likely to become synchronized in human-human tasks than human-machine tasks. Moreover, theta/alpha (6-12 Hz) amplitudes synchronized in the same temporal and lateral-parietal regions in each pair. Behavioral and inter-brain synchronizations were enhanced after human-machine tasks. These results indicate that inter-brain synchronizations are tightly linked to speech synchronizations between subjects. Furthermore, theta/alpha inter-brain synchronizations were also found in subjects while they observed human-machine tasks, which suggests that the inter-brain synchronization might reflect empathy for others' speech rhythms.