The cohomology of the group \(SL(n,\mathbb Z)\), \(n>1\), plays a fundamental role in geometry, topology and representation theory, while yielding many number theoretical applications: For instance, Borel used his description of \(H^*(SL(n,\mathbb Z))\) to compute the algebraic K-theory of the integers; whereas the (non-)vanishing of \(H^*(SL(n,\mathbb Z))\) tells a lot about the existence of certain automorphic forms. In this talk we will study the cohomology of \(SL(n,\mathbb Z)\), „right outside“ of what one calls the stable range. More precisely, we will show new non-vanishing results in degrees \(n-1\) and \(n\). As a byproduct, we will also answer a question, recently asked by F. Brown in this seminar for \(n=6\) and explain a phenomenon for \(n=8\), which has been considered by A. Ash. (This is joint work with N. Grbac.)