We present external-memory algorithms for differencing large hierarchical datasets. Our methods are especially suited to streaming data with bounded differences. For input sizes m and n and maximum output (difference) size e, the I/O, RAM, and CPU costs of our algorithm rdiff are, respectively, m + n, 4e + 8, and O(MN). That is, given 4e + 8 blocks of RAM, our algorithm performs no I/O operations other than those required to read both inputs. We also present a variant of the algorithm that uses only four blocks of RAM, with I/O cost 8me+18m+n+6e+5 and CPU cost O(MN).