The authors introduce several nonstandard hulls for topological vector spaces. These are defined using convex subrings of \({}^*\mathbb{R}\). If \(\mathbb{F}\) is such a subring and \(E\) is a topological vector space then \(p\in{}^*E\) is \(\mathbb{F}\)-bounded if for every neighbourhood \(U\) of \(0\) in \(E\) there is \(r\in\mathbb{B}\) outside the maximal ideal such that \(p\in {}^*U\). The \(\mathbb{F}\)-halo of \(0\) is defined to be \(\bigcap_{r,U}r{}^*U\), where \(r\) runs over all members not in the maximal ideal of \(\mathbb{F}\) and \(U\) runs through all neighbourhoods of \(0\). The nonstandard hull of \(E\) then is the quotient of the set of \(\mathbb{F}\)-bounded elements by the \(\mathbb{F}\)-halo of \(0\) endowed with a suitable topology. After establishing some elementary properties of this operation, the author turn to some examples: spaces of smooth functions and spaces of polynomials. In these applications, the choice of subring does not seem to affect the conclusions.