Some functional representation theorems for monadic $n$-valued Łukasiewicz algebras (qLk${}_n$-algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre Łukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027–1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLk${}_n$-algebras are obtained. Besides, rich qLk${}_n$-algebras are introduced and characterized. In addition,...