Transcranial alternating current stimulation (tACS) is the application of subthreshold, sinusoidal current to modulate ongoing brain rhythms related to sensory, motor and cognitive processes. Electrophysiological studies suggested that the effect of tACS applied at an alpha frequency (8-12 Hz) was state-dependent. The effects of tACS, that is, an increase in parieto-occipital electroencephalography (EEG) alpha power and magnetoencephalography (MEG) phase coherence, was only observed when the eyes were open (low alpha power) and not when the eyes were closed (high alpha power). This state-dependency of the effects of alpha tACS might extend to the aging brain characterized by general slowing and decrease in spectral power of the alpha rhythm. We additionally hypothesized that tACS will influence the motor cortex, which is involved in motor skill learning and consolidation. A group of young and old healthy adults performed a serial reaction time task (SRTT) with their right hand before and after the tACS stimulation. Each participant underwent three sessions of stimulation: sham, stimulation applied at the individual participant's alpha peak frequency or individual alpha peak frequency (iAPF; α-tACS) and stimulation with iAPF plus 2 Hz (α2-tACS) to the left motor cortex for 10 min (1.5 mA). We measured the effect of stimulation on general motor skill (GMS) and sequence-specific skill (SS) consolidation. We found that α-tACS and α2-tACS improved GMS and SS consolidation in the old group. In contrast, α-tACS minimally improved GMS consolidation but impaired SS consolidation in the young group. On the other hand, α2-tACS was detrimental to the consolidation of both skills in the young group. Our results suggest that individuals with aberrant alpha rhythm such as the elderly could benefit more from tACS stimulation, whereas for young healthy individuals with intact alpha rhythm the stimulation could be detrimental.