B757 CARGO LINER HAD A LESS THAN LEGAL SPACING WITH A FOREIGN ACR IN FOREIGN AIRSPACE.

Narrative

SHORTLY AFTER DEPARTING TAIPEI (TPE); TAIWAN ENRTE TO SINGAPORE (SIN) AND WHILE CLBING THROUGH FL330 TO OUR ASSIGNED ALT OF FL350 ON A DIRECT COURSE TO TNN VOR; AN APCHING ACFT (ACR ABC) AT FL330 RECEIVED A TCASII RA AND STARTED A DSNDING R TURN. ACR ABC PASSED BENEATH US SLIGHTLY TO OUR L. AT THE TIME; WE DID NOT KNOW FLT ABC'S ALT; AND RECEIVED NO TA FROM TPE CTL. WE DID HAVE VISUAL CONTACT WITH THE APCHING ACFT EARLY ON; WHICH BOTH ACFT ACKNOWLEDGED WITH THEIR LNDG LIGHTS. WE WERE ON TOP OF CLOUDS AT NIGHT AND WERE NOT ABLE TO VISUALLY ASCERTAIN ACR ABC'S ALT. DID NOT REALIZE THERE WAS A POTENTIAL CONFLICT UNTIL HE STARTED HIS DSCNT AND TURNED HIS LNDG LIGHTS BACK ON. OUR ACFT WAS NOT EQUIPPED WITH TCASII. TCASII ON BOTH ACFT MOST CERTAINLY WOULD HAVE MADE THIS NEAR MISS A NON EVENT. THE TPE CTLR NEVER PROVIDED ANY WARNING AND NEVER ACKNOWLEDGED AN ALT INCURSION; BUT PROMISED TO REVIEW THE TAPES WHEN TOLD A SAFETY RPT WOULD BE FILED. WE RPTED THE EVENT TO OUR COMPANY FLT OPS IN THE UNITED STATES VIA TELEPHONE AS SOON AS WE LANDED IN SIN.