In the present paper we consider the approximation of smooth functions from various classes with the help of entire functions of exponential type. We assume that our smooth functions f are defined on an union of countable set of segments {[an; bn]} lying on the real axis such that all of those segments are commensurable and all complementary intervals are commensurable too. Let ω be a modulus of continuity satisfying a classical Dini condition, namely Zx 0 ω(t) t dt + x Z∞ x ω(t) t 2 dt ≤ c · ω(x). We consider classes of functions f such that f is bounded on S n∈Z [an; bn] and for all r ≥ 0, x1, x2 ∈ In one has a property |f (r) (x2) − f (r) (x1)| ≤ cfω(|x2 − x1|), f (0) def = f. We denote through Tσ a set of entire functions of exponential type ≤ σ bounded on the real axis. The main result of our paper is following. Theorem. Let a function f and a modulus of continuity ω satisfy conditions mentioned above. Then for any σ ≥ 1 there exists a function Fσ ∈ Tσ such that for x ∈ S n∈Z [an; bn] one has an estimate |f(x) − Fσ(x)| ≤ cf d r 1+ 1 σ (x, [ n∈Z [an; bn])ω(d1+ 1 σ (x, [ n∈Z [an; bn])), where characteristic dρ(x, . . .) was introduced in our paper (Vestnik St. Petersburg Univ.: Math. 49, issue 4, 373–378 (2016)).