Abstract. Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e. contextfree grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g. suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACE-complete. This solves an open problem of Plandowski and Rytter. 