Abstract We study theP-interpolation property for certain local theory extensions, and use these results for proving $$\le $$ ≤ -interpolation in classes of semilattices with monotone operators. For computing the $$\le $$ ≤ -interpolating terms, we use a hierarchic approach. We use these results for the study of $$\sqsubseteq $$ ⊑ -interpolation in the description logics $$\mathcal{E}\mathcal{L}$$ EL and $$\mathcal{E}\mathcal{L}^+$$ EL+ .