We present sufficient conditions for the existence of a single stable controller to stabilize a set of n SISO plants : P-1, P-2,..., P-n (strong simultaneous stabilization). As is well known, this is equivalent to the existence of a single controller, not necessarily stable, to stabilize n+1 plants (simultaneous stabilization). The basic assumption required in this paper is that all the plants have the same unstable zeros. A practical example of where such an assumption holds is when each plant has the same pure delay, which is approximated by a non-minimum-phase rational function. The results here are applied to examples of this type.