AUTOPLT INDUCED PORPOISING LED TO AN RA RPT FROM ACR TFC BELOW. ALTDEV ALT EXCURSION FROM ASSIGNED.

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WE HAD JUST DSNDED TO 29000 FT FROM 31000 FT FOR TFC. AFTER A MINUTE OR SO; ATC ASKED OUR ALT. I TOLD HIM WE WERE AT 29000 FT; ACTUALLY WE WERE AT 28940 FT. ATC SAID 'I SHOW YOU AT 28700 FT.' THE CAPT HAD NOW CORRECTED THE 60 FT AND WE WERE AT EXACTLY 29000 FT. I; AGAIN; TOLD THE CTLR THAT WE WERE AT 29000 FT. AT THE SAME TIME THIS IS GOING ON; WE HAD A TA FOR TFC ABOUT 4.5 MI AT OUR 10 O'CLOCK POS AND 800 FT BELOW US. THAT TFC MOVED TO ABOUT 3 MI AND STILL AT 800 FT BELOW US. THAT IS THE LAST TIME I LOOKED AT THAT TFC ON TCASII. A WHILE LATER; THE ACR TFC CAME ON THE FREQ AND HAD SAID THAT THEY HAD A RA ON THEIR TCASII AND THAT IT WAS A (OUR COMPANY NAME) FLT. MY CAPT CALLED ATC AND ASKED IF THAT WAS US. ATC SAID IT WAS. WE WERE STILL AT 29000 FT. WE NEVER HAD A RA ON TCASII. CONTRIBUTING FACTORS: WERE LIGHT TO MODERATE TURB; THE ACR TFC MAY HAVE BEEN OFF ALT BY 100 FT; OR INCORRECT XPONDERS OR TCASII. WHILE DISCUSSING THE PROBS; THE CAPT AND I NOTICED THAT THE AUTOPLT WAS PORPOISING MINUS 200 FT TO PLUS 100 FT. THE CAPT HAND FLEW THE ACFT; THEN PUT THE AUTOPLT BACK ON; AGAIN IT PORPOISED. WE WERE IN MODERATE TURB. HE FLEW IT TO SMOOTH AIR. THE AUTOPLT DID FINE. THE AUTOPLT WAS WRITTEN UP IN OUR MAINT LOG. OUR ALT ALERT NEVER WENT OFF SO I DON'T THINK WE WERE 300 FT LOW. SUPPLEMENTAL INFO FROM ACN 317222: APPROX 1000 FPM DSCNT WAS MADE TO FL290. SHORTLY AFTER LEVELOFF; TCASII SHOWED 'TFC.' BASED UPON A CONVERSATION BTWN ACR FLC AND ATC; I ASKED ATC IF THEY HAD SHOWN A TFC CONFLICT; AND HE RESPONDED; 'YES; I SHOWED YOU AT FL287 AT ONE TIME.' WHILE THE FO AND I WERE DISCUSSING WHAT HAD TAKEN PLACE AND WHAT; IF ANYTHING; WE SHOULD DO ABOUT IT; I NOTICED OUR ACFT AT FL288. I FLEW THE ACFT WITH MANUAL INPUTS FOR A WHILE UNTIL WE FOUND SMOOTH AIR. I ELECTED TO WRITE UP THE AUTOPLT FOR MAINT ATTN UPON LNDG. WE GOT HIT BY LIGHTNING ON THE NEXT LEG; NOT MY DAY!