Summary: Let \(E\) be a topological vector space and consider, for any \(n\in\mathbb{N}\), the variational inequality: find \(u\in E\) such that \(f_n(u,w)+ \phi_n(u)\leq\phi_n(w)\) for any \(w\in E\), where \(f_n: E\to\mathbb{R}\) and \(\phi_n: E\to\mathbb{R}\cup\{+\infty\}\). The aim of this paper is, first, to give assumptions of minimal character on the convergence of \((f_n)_n\) and \((\phi_n)_n\) in order to obtain convergence results for the solutions of the above problems. Then, these results are applied both to variational inequalities involving singlevalued operators and to variational inequalities involving multivalued operators.