We extend the nonstandard hull construction of Luxemburg and we show that the proposed extension covers various other constructions such as the tracial and the weak nonstandard hull. We provide a novel proof that the tracial nonstandard hull of an internal von Neumann algebra is itself a von Neumann algebra. We prove that some extensively studied properties of C*-algebras are preserved and reflected by the nonstandard hull construction. Eventually, we show how to obtain hull--like representations of the two K--groups associated to the nonstandard hull of an internal C*-algebra.