Abstract: This article discusses the high-ordered stochastic and dual stochastic orders of real-valued random variables. Section 1 describes in brief the economical meanings of ordering random variables in the framework of utility theory and its dual theory. Section 2 is on the high-ordered order of real-valued random variables based on the distributions. Some specifications of this order in expected utility theory are reached. Section 3 deals with the high-ordered order of real-valued random variables based on the dual theory, mainly the dual moments, and its specification in Yarri’s equivalent measure of random variables are presented.