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The main goal of this paper is to characterize limit key polynomials for a valuation ν on K [ x ]. We consider the set Ψ α of key polynomials for ν of degree α. We set p to be the exponent characteristic of ν. Our first main result (Theorem 1.1) is that if F is a limit key polynomial for Ψ α , then the degree of F is p r α for some r ∈ N. Moreover, in Theorem 1.2, we show that there exist Q ∈ Ψ α and F a limit key polynomial for Ψ α , such that the Q -expansion of F only has terms which are powers of p. [ABSTRACT FROM AUTHOR]