Majority of the improper integrals we meet in practice are principal values in the sense of Cauchy. However, discontinuous proceses, especially noncomutative and nonasociative processes bring the idea of iterative boundary values $\lim_{\epsilon_i\to0}(\lim_{\epsilon_j\to0}f)$. In this paper we give a definition of the generalized principal value of the improper real integral, and its calculation.