Many different intercellular signaling pathways are known but, for most, it is unclear whether they can generate oscillating cell behaviors. Here we use time-lapse analysis of Drosophila embryogenesis to show that oenocytes delaminate from the ectoderm in discrete bursts of three. This pulsatile process has a 1 hour period, occurs without cell division, and requires a localized EGF receptor (EGFR) response. High-threshold EGFR targets are sequentially activated in rings of three cells, prefiguring the temporal pattern of delamination. Surprisingly, widespread misexpression of the relevant activating ligand, Spitz, is compatible with robust delamination pulses. Moreover, although Spitz ligand becomes limiting after only two pulses, artificially prolonging its secretion generates up to six additional cycles, revealing a rhythmic underlying mechanism. These findings illustrate how intercellular signaling and cell movements can generate multiple cycles of a cell behavior, despite individual cells experiencing only one cycle of receptor activation.