Summary: ``The purpose of this paper is to study strict positivity in the nonstandard hull of an internal normed Riesz space. Several characterizations are obtained for an element of the hull to be strictly positive. Particularly, it is shown that the nonstandard hull of an internal normed Riesz space has strictly positive elements if and only if it has an order unit. This result has an application to the double infinity problem in economics. It follows that the existence of equilibria in a nonstandard double infinity economy is equivalent to the existence of finite equilibira.''