Understanding sex differences in the use of task-related neural compensatory mechanisms in healthy elderly individuals and Alzheimer’s disease patients is necessary to improve early diagnosis and staging of the disease. Measuring participants’ brain activity at different frequencies with electroencephalography (EEG) in a resting state following a cognitive task might be a suitable measure to identify such differences, with early EEG-based biological signs (biomarkers). The present secondary data analysis investigated sex differences among healthy older adults and Alzheimer’s disease patients in the power of EEG signals at the alpha (8-13 Hz) and theta (6-8 Hz) frequency bands, using the alpha/theta ratio (TAR), with alpha divided into sub-bands: alpha1 (8-10 Hz) and alpha2 (10-13 Hz). Data was obtained from EEG signals with eyes open, sampled from the end of each trial of a cross-modal memory task. Participants (73 mild Alzheimer’s disease patients and 63 age-matched healthy controls) were repeatedly presented with a paired associated visual (image) and auditory (spoken word) stimulus and asked to make an Old and New decision for each stimulus pair. Compared with males, both healthy females and female patients showed higher post-task alpha1/theta ratio power. Moreover, patients were characterized by greater post-task alpha2/theta ratio power than healthy elderly adults. These results suggest that the benefits of female brain plasticity begin to deteriorate in females with mild Alzheimer’s disease and supports suggestions that Alzheimer’s disease patients recruit alternative neural processes to aid the completion of a task. It is hoped that future clinical trials account for such sex- and disease-related neural abnormalities, and that this will help the stratification of Alzheimer’s disease patients, early diagnosis, and monitoring of the disease.