Given a Tychonoff space X, let F (X) and A(X) be respectively the free topological group and the free Abelian topological group over X in the sense of Markov. In this paper, we consider two topological properties of F (X) or A(X), namely the countable tightness and G-base. We provide some characterizations of the countable tightness and G-base of F (X) and A(X) for various special classes of spaces X. Furthermore, we also study the countable tightness and G-base of some Fn(X) of F (X).2000 Mathematics Subject Classification. Primary 54H11, 22A05; Secondary 54E20; 54E35; 54D50; 54D55.