<p>Rellich and Hardy differential inequalities play important roles in harmonic analysis and applications to PDEs. Our aim in this manuscript is to study a generalization of these inequalities in the multilinear setting. Weighted Rellich inequalities in the one-dimensional case were derived by the authors in 2021. In this manuscript, two-weighted multilinear Rellich and Hardy differential inequalities in higher dimensional case are established. The results are derived, generally speaking, on nilpotent Lie groups <i>G</i> (homogeneous groups). The results are new even for the Abelian (Euclidean) case <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G=\mathbb {R}^{d}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>. As a corollary we get two-weighted multilinear Rellich and Hardy estimates for power weights. Results are obtained via the weighted inequalities for a class of multilinear fractional integrals involving Riesz potentials which are also studied in this paper.</p>