ACitation Excel experienced an NMAC with a military jet on arrival to STL.

Narrative

Lack of ATC separation of VFR and IFR traffic. While on the QBALL arrival to STL airport during cruise flight at 11;000 FT the TCAS alerted indicating a target at the two o'clock position with no altitude readout. The copilot visually picked up a military aircraft approximately 1-2000 FT low on a similar course passing right to left. The aircraft then pulled its nose up in a climb that was on a collision course with our aircraft. The copilot took immediate evasive action by disconnecting the autopilot; pulling the nose up in a climbing right turn to avoid the military aircraft. It passed from right to left with about 200 FT of lateral separation while climbing through our altitude. It was obvious to us the other pilot never saw our aircraft. ATC never provided any warning to us about the aircraft. I informed ATC of the near miss and acquired a number to call when on the ground. One thing is certain; if we had not been alerted by the TCAS and visually acquired the target aircraft a collision was certain. Also it was the copilot's quick and decisive action that saved the day.