MIL ACFT ON IFR FLT DOES NOT HAVE TRANSPONDER AND ENTERS ADJACENT FAC AIRSPACE WITHOUT COORD.

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AT APPROX XX05 PM CST I RELIEVED THE R-3 SPECIALIST AT ZME. HE HAD SECTORS 1 & 2 COMBINED AT THIS POS. DURING THE RELIEF BRIEFING HE POINTED TO A DATA BLOCK IN COAST TRACK JUST NE OF THE TULSA VOR. THE ACFT CALL SIGN WAS MLT X AND THE DATA BLOCK INDICATED HE WAS AT 9000. THE STRIP FOR MLT X SHOWED A DIRECT ROUTING TO HRT. THE SPECIALIST I WAS RELIEVING MOVED THE DATA BLOCK TO A POS JUST S; AND OUTSIDE OF; TUL APCHS AIRSPACE AND TOLD ME THAT WAS HIS APPROX POS BUT TOLD ME I PROBABLY SHOULD GET A POS RPT TO VERIFY HIS EXACT POS. THE CTLR I RELIEVED INFORMED ME MLT'S TRANSPONDER HAD FAILED. I ACCEPTED THE SECTOR AND TOOK IMMEDIATE ACTION TO PINPOINT MLT X BY ASKING FOR A RADIAL AND DME FROM THE RZC VORTAC. MLT X REPLIED HE WAS XING THE RZC 192 RADIAL AT 30 DME. I DISPLAYED HIS RTE ON MY PVD AND TOOK A RANGE BEARING FROM RZC AT APPROX THE RZC 192 RADIAL. IT TOOK ANOTHER COUPLE OF RANGE BEARINGS TO PINPOINT MLT X'S POS; JUST AT FSM APCHS BOUNDARY HEADED INTO THEIR AIRSPACE. I WAS NOT RECEIVING A PRIMARY TARGET ON MLT X AS THE RADAR SITE WHICH SERVES NW ARKANSAS IS BEACON ONLY. I IMMEDIATELY CALLED FSM APCH TO COORD AND THE CTLR INFORMED ME HE COULD SEE MLT X ON HIS PRIMARY AND HE WAS ALREADY SOME 5 TO 6 MIS INSIDE HIS AIRSPACE. IF THE RADAR SITE COULD BE UPGRADED TO INCLUDE PRIMARY RETURNS ALSO WE COULD AVOID A SIMILAR SITUATION IN THE FUTURE.