Waiting time jitter is a low-frequency phase jitter introduced whenever asynchronous digital signals are synchronized for multiplexing by pulse stuffing. It contains arbitrarily low frequency components and cannot be completely removed from the demultiplexed signals. In this paper the spectrum of waiting time jitter is derived, and supporting experimentally recorded waiting time jitter spectra are presented. A question of much engineering interest is at what rate waiting time jitter accumulates in a chain of multiplexer-demultiplexer pairs. A calculation based on the theoretical waiting time jitter spectrum shows that under reasonable conditions the rate at which the rms amplitude of the accumulated waiting time jitter grows is no greater than the square root of the number of multiplexer-demultiplexer pairs. Experimental data consistent with this upper bound are given.