Let E=∪k=1n[akbk]⊂ℝ; if n > 1, then we assume that the segments [a _k, b _k] are pairwise disjoint. Assume that the following property holds: E ∩ (E + 2πν) = ∅, ν ∈ ℤ, ν ≠ 0. Denote by H ^{ω + r}(E) the space of functions f defined on E such that |f ^(r)(x ₂) − f ^(r)(x ₁)| ≤ c _fω(|x ₂ − x ₁|), x ₁, x ₂ ∈ E, f ⁽⁰⁾ ≡ f. Assume that a modulus of continuity ω satisfies the condition∫0xω(t)tdt+x∫x∞ω(t)t2dt≤cω(x). We find a constructive description of the space H ^{ω + r}(E) in terms of the rate of nonuniform approximation of a function f ∈ H ^{ω + r}(E) by trigonometric polynomials if E and ω satisfy the above conditions.