Daily return series of Dow Jones Industrial Average Index (DJIA) and Shanghai Conposite Index are investigated using spectral analysis methods. The day of the week effect is found in the frequency domain in both stock markets. Time domain performances of the daily returns are also studied. Although both markets have a clear weekly component in the frequency domain, they show some different behaviors with respect to the day of the week effects. Daily return series of Dow Jones Industrial Average Index (DJIA) and Shanghai Conposite Index are investigated using spectral analysis methods. The day of the week effect is found in the frequency domain in both stock markets. Time domain performances of the daily returns are also studied Although both all have clear weekly component in the frequency domain, they show some different behaviors with respect to the day of the week effects.