LTSS BTWN OPPOSITE DIRECTION ACR ACFT AT CRUISE ALT E OF AMA.

Narrative

ENRTE FROM DENVER TO DALLAS FT WORTH (DFW); WE WERE DSNDED FROM FL370 TO FL330 AS WE APCHED AMARILLO. ATC ADVISED AFTER REACHING FL330 WE WERE CLRED TO CROSS 40 NM NW OF BRIDGEPORT VOR AT FL240 ON THE BOIDS 2 ARR TO DFW. WE PLANNED TO BEGIN OUR DSCNT 25 NM NW OF WICHITA FALLS. AT ABOUT 80 NM OUT OF WICHITA FALLS; CENTER POINTED OUT TFC IN THE OPPOSITE DIRECTION AT OUR 10 O'CLOCK POS; LEVEL AT FL310. WE IDENTED THE TFC VISUALLY AND SO ADVISED ATC. VERY SHORTLY AFTER THAT; AS THE TFC PASSED OFF OUR L SIDE; ATC ASKED US OUR ALT. WE WERE STILL LEVEL AT FL330 AND SO NOTED IT ON ALL 3 ALTIMETERS. WE ADDITIONALLY NOTICED THE TCASII INDICATING OUR 9 O'CLOCK TFC AS PASSING 5 MI TO OUR L AND THE ALT DIFFERENCE INDICATED 1900 BELOW US. CENTER THEN ASKED US TO VERIFY OUR ALT AND AGAIN WE RECHKED ALL ALTIMETERS; 29.92 SETTINGS AND TRANSPONDER ALT RPTING SWITCH ON. WE AGAIN CONFIRMED FOR ATC THAT WE WERE AT FL330 LEVEL. WE WERE ADVISED THAT THE CENTER'S EQUIP HAD INTERMITTENTLY GIVEN OFF A CONFLICT ALERT. CENTER DID NOT SOUND TOO CONCERNED ABOUT THE SITUATION. I WAS HOWEVER AWARE OF THE SERIOUSNESS OF SUCH ENCOUNTERS WITH OTHER PLTS AND CTLRS. WE BEGAN OUR DSCNT TO FL240 ABOUT 25 MI LATER AND WAS REASSURED OF NO PROBLEM EXISTING.