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A functional central limit theorem is proved for the centered Occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α＜ d ＜ 2α (0 ＜α≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d = 2α and higher dimensions d ＞ 2α, the limiting process is Brownian motion.