In this paper, asymptotic stability properties of implicit Runge Kutta methods for delay differential equations are considered with respect to the test equation $y'(t) = a y(t) + b y(t-1)$ with $a,b in C$. In particular, we prove that symmetric methods and all methods of even order cannot be unconditionally stable with respect to the considered test equation, while many of them are stable on problems where $a in R$ and $binC$. Furthermore, we prove that Radau IIA methods are stable on the subclass for equations where $a = alpha + i gamma$ with $alpha, gamma in R$, $gamma$ sufficiently small, and $bin C$.