In this book, we study the notions of Smarandache n-structure CIalgebras and Smarandache weak BE-algebras. Smarandache algebraic structures have been studied in a series of eleven books by W. B. Vasantha Kandasamy, one book by Jaiyeola Temitope Gbolahan, and tens of more books by W. B. Vasantha Kandasamy and Florentin Smarandache, including the neutrosophic algebraic structures as well. The study of Smarandache algebraic structures has caused a shift of paradigm in the study of algebraic structures. Smarandache algebraic structures simultaneously analyses two or more distinct algebraic structures.