OPERROR OCCURRED BTWN RPTR'S CLBING B767ER AND AN ACR B747 IN LEVEL FLT. CTR CTLR WAS UNAWARE OF THE B747 WHEN CLRNC WAS ISSUED FOR RPTR'S B767 TO CLB TO FL370 FROM FL330. ACFT PASSED WITH LTSS.

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UPON CHKING IN WITH MUSCAT CTL WE WERE ASKED IF WE COULD ACCEPT FL370 AS FL330 (OUR CURRENT ALT) WAS UNAVAILABLE OVER MAROB INTXN (USING THE 3/4 HIGH CHART). THE FMS INDICATED WE COULD ACCEPT FL370; BUT IT WOULD BE BEST TO DELAY THE CLB A LITTLE IF POSSIBLE. WE WERE 387 NM FROM MAROB. MUSCAT CTL CLRED US TO TEMPORARILY REMAIN AT FL330. WE CONTINUED AT FL330 UNTIL PASSING SEEB (MCT 114.5). MUSCAT SWITCHED US TO 124.55. ON 124.55 MUSCAT CTL SAID 'ACR X; CLB TO AND MAINTAIN FL370.' PNF TOLD MUSCAT 'ACR X LEAVING FL330 FOR FL370.' A 500-1000 FPM INITIAL CLB RATE WAS ESTABLISHED. NO TA'S WERE ISSUED BY MUSCAT. ON INITIAL CLB WE WERE IN A THIN CIRRUS LAYER. APCHING FL340 AN ONCOMING OPPOSITE DIRECTION ACFT ABOVE US TURNED ON HIS BRIGHT WHITE LIGHTS. WE RESPONDED WITH OUR LIGHTS. THE ACFT PASSED OVER AND A LITTLE TO THE L OF US AS WE REACHED FL340 IN OUR CLB; NOW CLR OF THE CLOUDS. THERE WAS NO INDICATION ON TCASII. WE PASSED THROUGH THE ACFT'S CONTRAILS AT FL350 AND CONTINUED OUR CLB TO FL370 AS ASSIGNED. WE QUERIED MUSCAT CTL ABOUT THE POTENTIAL CONFLICT WITH THE UNKNOWN ACFT AT FL350. MUSCAT SAID THERE WERE NO ACFT NEAR OUR POS AT FL350 AND THAT THE CLOSEST ACFT WAS AT FL310. WE TOLD MUSCAT THAT WE HAD DEFINITELY PASSED AN ACFT THAT WAS AT FL350. VERY SHORTLY THEREAFTER MUSCAT CALLED AND SAID THEY HAD JUST PICKED UP AN UNKNOWN ACFT AT FL350 OVER MCT. MUSCAT ESTABLISHED THAT THE ACFT'S CALL SIGN WAS ABC (ACR Y). ABC VERIFIED THEY WERE FLYING AT FL350. MUSCAT CTL INFORMED ABC THAT THEY HAD JUST PASSED ACR Y IN A REQUIRED CLB FROM FL330 TO FL370. MUSCAT ASKED ABC FOR THEIR CLRNC AND ABC REPLIED THEY HAD BEEN CLRED FROM OVER MAROB TO MCT AT FL350. MUSCAT CTL SAID THEY WOULD INVESTIGATE THE INCIDENT. DUE TO OUR POS WHEN WE ACHIEVED VISUAL CONTACT; NO EVASIVE ACTION WAS NECESSARY. HAD OUR CLB RATE BEEN GREATER AND IF VISUAL CONTACT HAD NOT BEEN POSSIBLE; A POTENTIAL HAZARD COULD HAVE BECOME VERY SERIOUS.