Some functional representation theorems for monadic n-valued Luk asiewicz algebras (qLkn-algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre L ukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027–1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLkn-algebras are obtained. Besides, rich qLkn-algebras are introduced and characterized. In addition, a third theorem for these algebras is presented and the relationship between the three theorems is shown.