B767 FLT CREW AT FL350 REPORTS TCAS RA WITH CLIMBING A340 NEAR GAPOX ON UG853. TCAS RA IS COMPLIED WITH TO ACHIEVE A 1000 FOOT VERTICAL SEPARATION AT CPA.

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WHILE ENRTE WE RECEIVED A TA AT THE 8 O'CLOCK POS. WE ESTABLISHED VISUAL CONTACT WITH ACFT (AT NIGHT). THIS WAS FOLLOWED BY AN RA APPROX 10 SECONDS LATER WITH A DSND COMMAND. PF COMPLIED BY PUTTING ACFT IN A 1000 FPM DSCNT TO THE GREEN BAND ON THE VSI. AFTER ABOUT 2 MINS; AND CLR OF OTHER ACFT WE RETURNED TO FL350. I HAD THE OTHER ACFT IN SIGHT DURING THIS MANEUVER. WE HAD MADE AN INFLT BROADCAST PER AFRICA THEATRE INSTRUCTIONS 5 MINS BEFORE THE GAPOX FIX. WE HEARD NO IFB FROM OTHER ACFT ON THE 126.9 IFB FREQ. THE OTHER ACFT; AN ACR Y; A340; CONTACTED US ON IFB FREQ 126.9; ABOUT A MIN OR SO AFTER THE RA TOOK PLACE. HE RPTED US IN SIGHT ALSO AS HE WAS CLBING TO FL390. HE RECEIVED A CLB RA WHICH HE FOLLOWED. THE ACR Y ACFT WAS FLYING DIRECT; NOT ON AIRWAYS AND CROSSED OUR AIRWAY UG853 BTWN PUBLISHED FIXES AND APCHED US FROM THE 8 O'CLOCK POS XING BEHIND OUR FLT PATH. WE WERE/HAD BEEN ESTABLISHED ON UG853 WITH A 2 MI R OFFSET AT TIME OF CONFLICT. THE WX RADAR WAS IN WX/TCAS MODE AS A PRECAUTION FOR UNSEEN (AT NIGHT) TSTMS. THIS PUT OUR ACFT AT THE BOTTOM OF THE WX RADAR DISPLAY NOT SHOWING THE OTHER ACFT WHICH WOULD BE OFF BOTTOM L SIDE OF WX RADAR DISPLAY.