We describe a new method to grow epitaxial semiconductor alloys with continuously variable composition, while using a single pulsed laser ablation target of fixed composition. Epitaxial ZnSe1−xSx films with continuously variable sulfur content, x, were grown by ablating a ZnSe target through low‐pressure ambient H2S gas. The sulfur content was easily controlled in the range 0<x<0.18 by varying the H2S partial pressure from 0 to 45 mTorr, for films grown at 325 °C. ZnSe1−xSx films differing in composition by as much as x=0.52 from the pure ZnSe target have been grown at 400 °C. We have used this method to grow heteroepitaxial structures with continuously graded or periodically repeating, abrupt compositional changes (compositional superlattices). This development removes the principal barrier to pulsed‐laser ablation (PLA) growth of compositionally graded semiconductor thin‐film materials, namely that the film and target normally have the same composition. The method appears to have broad application for PLA growth of other compound semiconductor films and heterostuctures, as well as to dope individual layers.