We extend the notion of homomorphisms and characters to $$n$$ n -homomorphisms and $$n$$ n -characters on algebras, and then show that some properties of characters are also valid for $$n$$ n -characters on commutative $$lmc$$ l m c topological algebras, and the space of continuous $$n$$ n -characters $$M_{(A,n)}$$ M ( A , n ) is relatively compact in $$A'$$ A ′ (the dual space of $$A$$ A ), with the weak* topology (Gelfand topology), whenever $$A$$ A is a commutative $$lmc$$ l m c $$Q$$ Q -algebra. We also find relations between characters, $$n$$ n -characters, and continuous $$n$$ n -characters on commutative Fréchet algebras. Let $$B$$ B be a topological algebra and $$(A_{\alpha },\varphi _{\beta \alpha })$$ ( A α , φ β α ) (resp. $$(A_{\alpha },\varphi _{\alpha \beta })$$ ( A α , φ α β ) ) be an inductive system (resp. a projective system) of topological algebras. Then we obtain relations between $$n-Hom(A_{\alpha },B)$$ n - H o m ( A α , B ) and $$n-Hom(A,B)$$ n - H o m ( A , B ) , or between , the inductive limit, and $$M_{(A,n)}$$ M ( A , n ) , where , is the inductive limit (resp. $$A=\varprojlim A_{\alpha }$$ A = lim ← A α , is the projective limit) and $$n-Hom(A_{\alpha },B)$$ n - H o m ( A α , B ) (resp. $$n-Hom(A,B)$$ n - H o m ( A , B ) ), is the space of all continuous n-homomorphisms from $$A_\alpha $$ A α (resp. $$A$$ A ) into $$B$$ B .