Alpha waves, one of the major components of resting and awake cortical activity in human electroencephalography (EEG), are known to show waxing and waning, but this phenomenon has rarely been analyzed. In the present study, we analyzed this phenomenon from the viewpoint of excitation and inhibition. The alpha wave envelope was subjected to secondary differentiation. This gave the positive (acceleration positive, Ap) and negative (acceleration negative, An) values of acceleration and their ratio (Ap-An ratio) at each sampling point of the envelope signals for 60 seconds. This analysis was performed on 36 participants with Alzheimer’s disease (AD), 23 with frontotemporal dementia (FTD) and 29 age-matched healthy participants (NC) whose data were provided as open datasets. The mean values of the Ap-An ratio for 60 seconds at each EEG electrode were compared between the NC and AD/FTD groups. The AD (1.41 ±0.01 (SD)) and FTD (1.40 ±0.02) groups showed a larger Ap-An ratio than the NC group (1.38 ±0.02, p<0.05). A significant correlation between the envelope amplitude of alpha activity and the Ap-An ratio was observed at most electrodes in the NC group (Pearson’s correlation coefficient, r = -0.92 ±0.15, mean for all electrodes), whereas the correlation was disrupted in AD (-0.09 ±0.21, p<0.05) and disrupted in the frontal region in the FTD group. The present method analyzed the envelope of alpha waves from a new perspective, that of excitation and inhibition, and it could detect properties of the EEG, Ap-An ratio, that have not been revealed by existing methods. The present study proposed a new method to analyze the alpha activity envelope in electroencephalography, which could be related to excitatory and inhibitory neural activity.