We consider three classes of N-functions: (Δ'), the class of functions satisfying the Δ' condition, (Δ2), the class of functions satisfying the Δ2 condition, and (MΔ), the class of functions M(u) satisfying the condition:\(\mathop {\lim }\limits_{u \to \infty }\) ln M (u) / ln u = p < ∞. We establish the connection between the class of powers and the class of N-functions M(u) which belong to the class (Δ') together with their complementary functions and we also establish the connections between the classes (Δ'), (MΔ) and (Δ2).