Abstract. Processing compressed strings without decompression is often essential when dealing with massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to Lempel–Ziv compression. For an SLP-compressed text of length m, and an uncompressed pattern of length n, C´egielski et al. [4] gave an algorithm for local subsequence recognition running in time O(mn2 log n). We improve the running time