ACR X TCASII RA HAD LTSS FROM CPR Y CLB TO SAME ALT. EVASIVE ACTION TAKEN. PLTDEV. SYS ERROR. TCASII LOGIC CHANGE IN RA INSTRUCTION.

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APCHING ADM I NOTICED A TCASII TARGET SSW (PROCEEDING NE) OF ADM AT FL350. I THOUGHT TO MYSELF THIS WAS WHY WE HAD NOT RECEIVED OUR DSCNT CLRNC YET. AS WE PASSED ADM AND INTERCEPTED THE OUTBOUND LEG I NOTICED THE TCASII TARGET WAS NOW CLBING AND INDICATED A READOUT OF FL360. AT FL360 THE TREND ARROW ON THE TARGET BEGAN TO FLUCTUATE BTWN UP; DOWN AND NEUTRAL. THE TARGET WAS STILL ABOUT 10 PLUS MI AWAY AT OUR 12:30 - 1 O'CLOCK POS. THE TREND ARROW THEN WENT UP AND STAYED UP WITH THE ALT CLOSURE RATE DECREASING. I ASKED THE FO TO INQUIRE ABOUT THE TFC. HE DID SO AND ATC INDICATED THEY HAD NO TFC. I THEN DIRECTLY ASKED ATC 'YOU SHOW NO TFC AT OUR 1 O'CLOCK POS AND 10 MI?' (THE TARGET HAD NOW CLOSED TO ABOUT 7 MI.) THERE WAS NO RESPONSE FROM ATC. THE TARGET WAS STILL CLOSING SO I INITIATED A 20 DEG HDG CHANGE TO THE R USING THE HDG SELECT MODE ON THE AUTOPLT. I TOLD THE FO TO INFORM ATC OF OUR TURN. ABOUT THIS TIME WE GOT A TCASII ALERT AND I INCREASED BOTH THE AMOUNT OF HDG CHANGE AND ANGLE OF BANK (FROM 10 DEGS TO 30 DEGS). BY NOW THE TARGET WAS WITHIN 5 MI; STILL ON AN INTERCEPT HDG AND STILL CLBING. THE TCASII RA FUNCTION WENT OFF AND INITIALLY SAID 'DSND.' I DISCONNECTED THE AUTOPLT AND AUTO THROTTLES AND COMMENCED A DSNDING R TURN WHEREUPON THE TCASII CHANGED ITS MIND AND TOLD US TO 'CLB; CLB NOW.' I STARTED TO CLB (TOWARDS THE RA COMMAND BARS) BUT IMMEDIATELY BECAME AWARE OF A BUFFET. I PUSHED THE NOSE OVER AND ROLLED THE AIRPLANE TO APPROX 40 DEGS OF BANK. WHILE ALL OF THIS WAS OCCURRING I WAS AWARE OF ATC TELLING US TO IMMEDIATELY TURN TO A HDG OF 280 DEGS FOR TFC. I TOLD ATC WE WERE IN A TURN AND DSNDING FOR TFC AVOIDANCE. AS WE WERE TURNING I LOOKED OUT MY SIDE WINDOW AND SAW WHAT APPEARED TO BE A CPR Y JET IN A HARD R TURN WITHIN 1 MI OF OUR POS. WE ROLLED OUT ON A 280 DEG HDG AND LEVELED AT FL350 PUTTING US DIRECTLY ON A HDG TO REENTER THE WX WE HAD JUST DEVIATED AROUND! WE ASKED ATC IF WE COULD STAY AT FL350 WHEREUPON THE CTLR INDICATED 'NEGATIVE; NEGATIVE; CLB TO FL370.' I COMMENCED A CLB TO FL370 AND INFORMED ATC WE NEEDED TO TURN L FOR WX AVOIDANCE.