[en] In the theory of functions, an asymptotic spot of a function f is defined to be a pair { a,Γ}, where a element of C-bar and Γ is a continuous curve such that f(z)→a (z→∞, z element of Γ). In this paper we introduce a new notion of a strong asymptotic spot. Using this notion, we extend some results of Ahlfors (concerning asymptotic spots of entire functions of finite order) to functions of infinite order. We obtain exact estimates for the number of different strong asymptotic spots { ∞,Γ_j} of entire functions of finite or infinite lower order