Second Order Freeness is a notion of independence which was developed to give an algebraic framework to the limit laws of fluctuations in Random Matrices. Building such a framework should allow to calculate the fluctuation moments of many random matrix ensambles built from the known ones, in particular, products or sums. However, until recently, not many examples were known where one could calculate the fluctuations moments explicitly.

In this talk we develop further the combinatorial machinery of second order cumulants to provide various examples based on second order versions of two important classes: even elements and $R$-diagonal elements.