A subset A of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence {x n } ∞ n=1 in E contained in A converges to a point x ∈ A (a point x ∈ E). Asanov and Velichko proved that if X is countably compact, every functionally bounded set in C p (X) is relatively compact, and Baturov showed that if X is a Lindelöf Σ -space, each countably compact (so functionally bounded) set in C p (X) is a monolithic compact. We show that if X is a Lindelöf Σ -space, every functionally bounded (relatively) sequentially complete set in C p (X) or in C w (X), i. e., in C k (X) equipped with the weak topology, is (relatively) Gul'ko compact. We get some consequences.