The pulse displacements produced by timing errors in a chain of regenerative repeaters (using tuned-circuit timing filters) are represented by a linear transformation of the pulse displacements at the output of the first repeater. To facilitate the discussion of the general problem, the simpler case of periodic pulse trains is considered first. For this case it is shown that while the mean value tends to infinity, the central moments of the pulse displacements remain bounded as the number of repeaters approaches infinity. Further results are obtained, which show that all the moments of the spacing jitter remain bounded for an indefinitely long string of repeaters. Finally, the misalignment in the jitter at any given repeater is represented by a simple expression which shows that the essential component in the misalignment is flat delay. The general problem of random pulse trains, infinite in length, is discussed in Part II in this issue. The results obtained for the general case are quite different from those obtained for the periodic case. The variance is unbounded in this case except for pulse trains with certain special restrictions. The computational aspects for the evaluation of jitter accumulation will be discussed in a subsequent paper.