FLC OF A B727 CLBED IN RESPONSE TO A TCASII RA AND WAS GIVEN A TA AND TURNED BY ATC. ANOTHER ACFT WAS CLBING THROUGH THEIR ALT IN THE OPPOSITE DIRECTION.

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AT APPROX XA40 ON SEP/FRI/00; WE RECEIVED A TCASII ALERT AND SUBSEQUENT ADVISORY AT FL260 WHILE FLYING FROM CIA (ROME) TO TSF (TREVESO; ITALY). THE OPPOSING ACFT HAD ERRONEOUSLY BEEN GIVEN INSTRUCTIONS TO CLB THROUGH FL260 TOO CLOSE TO OUR ACFT. THE ADVISORY WAS GIVEN JUST AS THE ACFT CAME INTO THE MAX RANGE OF THE TCASII SCOPE (6 MI) ON OUR ACFT. AT THE SAME TIME THE ADVISORY WAS GIVEN; THE CTLR GAVE US AN IMMEDIATE HEADING CHANGE TO TRY TO AVOID THE CONFLICT. HE ALSO GAVE INSTRUCTIONS TO THE OTHER ACFT. THE COMBINATION OF THE CTLR AND THE TCASII CAUSED A LOT OF CONFUSION IN THE COCKPIT. THE GOOD PART WAS THAT THE WX WAS EXCEPTIONALLY CLR AND WE WERE ABLE TO PICK UP THE OTHER ACFT IN TIME TO AVOID IT. IT WAS OBVIOUSLY THE CTLR'S FAULT AND HE KNEW IT. HE ASKED US SEVERAL TIMES IF WE WERE GOING TO FILE A RPT; AND WHILE HE TRIED TO TALK US OUT OF IT; WE ASSURED HIM THAT WE WOULD. IT WAS FELT BY ALL THE CREW MEMBERS THAT THE 6 MI RANGE ON THE TCASII WAS VERY INADEQUATE; ESPECIALLY FOR HEAD-ON SITS AS DESCRIBED ABOVE. AS BEST AS CAN BE REMEMBERED; THE FIRST INDICATION THAT WE GOT ON THE TCASII SCREEN SHOWED THAT THE OTHER ACFT WAS 600 FT BELOW US AND CLBING. IT WAS ABOUT THIS SAME TIME THAT WE GOT 'TFC; TFC' IMMEDIATELY FOLLOWED BY 'PULL UP.' IT IS FELT THAT HAD THE SCREEN HAD A LARGER RANGE; WE WOULD HAVE BEEN ABLE TO PICK UP THE ACFT SOONER AND WOULD HAVE BEEN MORE COMFORTABLE THROUGHOUT THE WHOLE EVOLUTION. BASICALLY; THE TCASII SCREEN WAS ALMOST NO HELP AS THE RANGE WAS TOO SHORT AND THINGS WERE HAPPENING TOO FAST.