If \(E\) is an internal normed space, \(E^{\sharp}\) is its nonstandard hull, and \(A\: E\to E\) is an internal linear operator with limited norm then there exists a well-defined operator \(A^{\sharp}\: E^{\sharp}\to E^{\sharp}\) called the nonstandard hull of \(A\). The principal difficulty arises for \(A\) with unlimited norm. Such an operator defines no operators in the nonstandard hull immediately, since the elements with infinitesimal norm may be transformed into elements with noninfinitesimal norm. In the article under review, for an internal symmetric operator \(A\) defined on a hyperfinite-dimensional Euclidean space \(E\), the authors construct an essentially selfadjoint (unbounded in general) operator \(A^{\sharp}\) on \(E^{\sharp}\) which can be regarded as the nonstandard hull of \(A\). This construction is justified by the following natural properties: (1) if the norm \(\|A\|_{in}\) is limited then \(A^{\sharp}\) coincides with the usual nonstandard hull of \(A\); (2) if \(f\) is a standard bounded continuous function then the nonstandard hull of the bounded operator \({}^{*}f(A)\) coincides with \(f(A^{\sharp})\) on the domain of \(A^{\sharp}\) (in particular, this is valid for the resolvents of the operator \(A\)); (3) the spectral projections of the operator \(A^{\sharp}\) coincide with the nonstandard hull of the spectral projections of \(A\).