Our aim in this paper is to deal with Sobolev’s embeddings for Musielak–Orlicz–Sobolev functions in W01, for Ω ⊂ RN, as extensions of Harjulehto and Hästö (Publ Mat 52:347–363, 2008), Hästö (Math Res Lett 16(2):263–278, 2009) and Hästö et al. (Glasg Math J 52:227–240, 2010). Here Φ is a function such that ϕ(x, t) = t- 1Φ (x, t) is uniformly almost increasing positive function of t&gt
0.