This text constitutes the thoroughly refereed post-proceedings of the Third International Andrei Ershov Memorial Conference, PSI'99, held in Akademgorodok, Novosibirsk, Russia, in July 1999. The 44 revised papers, presented together with five revised full invited papers, were carefully reviewed and selected from a total of 73 submissions. The papers are organized in sections on: algebraic specifications; partial evaluation and super compilation; specification with states; concurrency and parallelism; logic and processes; languages and software; database programming; object-oriented programming; constraint programming; model checking and program checking; and artificial intelligence.