It is shown that stable linear gyroscopic systems of the form Mx" + Tx' + Kx = 0 ( M > 0) alway become unstable when an arbitrarily small delay is introduced in the gyroscopic term. In the case where K is negative definite, then the system will be unstable for all positive delays. On the other hand, examples are given showing that some of these systems may actually become asymptotically stable for larger values of the delay parameter.