Consider an \(m\)-server queue with general stationary and ergodic input and a general work-conserving discipline, and let \(E W\) denote the mean waiting time (in stationarity or in the sense of Cesaro averages). It is shown that even with bounded service times and an arbitrarily small traffic intensity it may occur that \(E W=\infty\), and mixing conditions are given excluding this phenomenon in the special case of the LCFS- discipline.