Summary: We consider \(\overline\nabla\)-harmonic curves and surfaces in Euclidean \(n\)-spaces \(\mathbb{E}^n\). We prove that every weak biharmonic curve is \(\overline\nabla\)-harmonic. We also show that every 1-parallel surface in \(\mathbb{E}^4\) is \(\overline\nabla\)-harmonic, but the converse is not true. Finally, we give the necessary condition for Vranceanu’s surface to become \(\overline\nabla\)-harmonic.