For cone preserving linear operators T the asymptotic behaviour of the terms \(T^ nf/\| T^ nf\|\) as \(n\to \infty\) is reviewed. For \(C_ 0\)-semigroups \((T(t))_{t\geq 0}\) of cone preserving operators new and surprising results on the asymptotic behaviour of \(T(t)f/\| T(t)f\|\) as \(t\to \infty\) are obtained.