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The retention of a new sequential motor skill relies on repeated practice and subsequent consolidation in the absence of active skill practice. While the early phase of skill acquisition remains relatively unaffected in older adults, posttraining consolidation appears to be selectively impaired by advancing age. Motor learning is associated with posttraining changes of oscillatory alpha and beta neuronal activities in the motor cortex. However, whether or not these oscillatory dynamics relate to posttraining consolidation and how they relate to the age-specific impairment of motor consolidation in older adults remains elusive. Transcranial alternating current stimulation (tACS) is a noninvasive brain stimulation technique capable of modulating such neuronal oscillations. Here, we examined whether tACS targeting M1 immediately following explicit motor sequence training is capable of modulating motor skill consolidation in older adults. In two sets of double-blind, sham-controlled experiments, tACS targeting left M1 was applied at either 10 Hz (alpha-tACS) or 20 Hz (beta-tACS) immediately after termination of a motor sequence training with the right (dominant) hand. Task performance was retested after an interval of 6 hours to assess consolidation of the training-acquired skill. EEG was recorded over left M1 to be able to detect local after-effects on oscillatory activity induced by tACS. Relative to the sham intervention, consolidation was selectively disrupted by posttraining alpha-tACS of M1, while posttraining beta-tACS of M1 had no effect on delayed retest performance compared to the sham intervention. No significant postinterventional changes of oscillatory activity in M1 were detected following alpha-tACS or beta-tACS. Our findings point to a frequency-specific interaction of tACS with posttraining motor memory processing and may suggest an inhibitory role of immediate posttraining alpha oscillations in M1 with respect to motor consolidation in healthy older adults.