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For a Tychonoff space X, we denote by C_k (X) the space of all real-valued continuous functions on X with the compact-open topology. A subset A ⊂ X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A. A space C_k (X) is selectively sequentially separable (in Scheepers’ terminology: C_k (X) satisfies S_fin(S, S)) if whenever (S_n: n ∈ N) is a sequence of sequentially dense subsets of C_k (X), one can pick finite F_n ⊂ S_n (n ∈ N) such that∪ {F_n: n ∈ N} is sequentially dense in C_k (X). In this paper, we give a characterization for C_k (X) to satisfy S_fin(S, S). © 2019, Hacettepe University. All rights reserved.