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The paper reviews briefly the methods of generating atomic time and the errors inherent in the resulting scales. An atomic clock consists of an atomic frequency standard and an "integrator" to accumulate the phase of the signal. Because of noise perturbing the instantaneous frequency, an ensemble of identical atomic clocks will show a distribution of (epoch) times which is unbounded as the system evolves in time. The recognition of this problem has important consequences in national and international coordination of time scales and the construction of average atomic time scales. Also of significance is the not completely resolved question of weighting of individual standards in the construction of average time scales. In spite of these difficulties, it is pointed out that through coordination and proper data handling, most of the advantages of astronomical time scales can be realized by atomic time scales. A statement of some of the problems facing any attempts at coordination is presented without any suggested solutions.