ACR MD80 FLC OBSERVES TCASII TFC CLBING FROM BENEATH IN APPARENT CONFLICT WITH THEM AND NOTIFIES ARTCC RADAR CTLR. CLBING B757 ALSO RECEIVES TCASII ALERT AND STOPS CLB. AFTER CONFLICT IS RESOLVED CTLR CLBS B757 TO HIGHER ALT. PICS OF BOTH ACFT STATE RECOMMENDATIONS TO CORRECT INCIDENT.

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ACFT X IN CRUISE AT FL350; RECEIVED TCASII; NOTED TARGET 1100 FT BELOW; CONVERGING AND CLBING. CALLED ANC ON 133.6 IMMEDIATELY AND RPTED CONFLICT AND INTENTION TO CLB. ACFT Y RESPONDED THAT THEY WERE STOPPING CLB AND DSNDING. CLOSEST ENCOUNTER WAS 2 MI; 800 FT VERT; AND VERT SEPARATION INCREASED TO MORE THAN 1000 FT AS ACFT Y PASSED UNDERNEATH. WE DID NOT CLB (NO RA) BECAUSE VERT CLOSURE STOPPED AND BEGAN INCREASING. ACFT Y RESUMED CLB TO FL370 AFTER HE PASSED UNDERNEATH US. RECOMMENDATION: 1) FAA/ARTCC COMPUTER EARLY RECOGNITION SOFTWARE TO IDENT CONFLICTING CLRNCS LONG BEFORE CONFLICT OCCURS. 2) I AM RECOMMENDING TO ACFT X COMPANY THAT WE ENACT POLICY IMMEDIATELY TO MAKE ALT CALLS MANDATORY; EVEN WHEN CONTACTING SAME CTLR ON A NEW FREQ IN SAME CTLR'S AIRSPACE. SITUATIONAL AWARENESS TO OTHER CREWS. 3) FAA REVIEW POLICY TO ENSURE ALL PLTS RPT ALT ON INITIAL CALL TO SAME CTLR AFTER FREQ CHANGE. NOTE: #2 AND #3 REFER MOSTLY TO NIGHTS WHEN 1 CTLR CTLS SEVERAL SECTORS. SUPPLEMENTAL INFO FROM ACN 415652: CLBING OUT OF PANC TO FL370; NOTICED TCASII TFC AT 25 MI AT FL350. AT FL335; NOTICED HE WAS GETTING UNUSUALLY CLOSE. WE STARTED TO LEVEL OFF AND THEN DSNDED TO AVOID CONFLICT. ATC AND OTHER ACFT NOTICED SIT AT ABOUT SAME TIME. OTHER ACFT SAID THEY WERE CLBING AND ATC TOLD US TO DSND; WHICH WE WERE ALREADY DOING. OUR PEAK ALT WAS FL339. AFTER CONFLICT WAS CLR; ATC AGAIN CLRED US TO CONTINUE CLB TO FL370. DURING THIS WE HAD A 'NON THREATENING PROX TFC' TCASII ALERT. POSSIBLE FACTORS: 1) ANC RADAR HAD SOME OUTAGES DURING THAT TIME FRAME WHICH MAY OR MAY NOT HAVE BEEN A FACTOR. OTHER ACFT MAY HAVE BEEN FLYING FROM A NON RADAR ENVIRONMENT. 2) CTLR WAS TALKING TO OTHER ACFT AND I THINK HE WAS CTLING OTHER ACFT ON A SEPARATE RADIO FREQ; WHICH SOMETIMES MAKES COM A LITTLE MORE DIFFICULT.