What was found
(CAN) WHILE VMC AT FL350 IN LEVEL FLIGHT NEAR THE AUTUN VOR, AIRCRAFT EXPERIENCED AT FULL TCAS ADVISORY & RESOLUTION. FIRST A TARGET DISPLAYED ON THE IVSI AT THE 2-3 O'CLOCK POSITION AT 2-3 NM RANGE AT THE SAME ALTITUDE, ACCOMPANIED BY AN AURAL WARNING. APPROXIMATELY 2 SECONDS LATER THE IVSI/TCAS LIT UP RED DIRECTING A CLIMB ACCOMPANIED WITH AN AURAL CLIMB COMMAND. VISUAL CONFIRMATION COMBINED WITH UNREALISTIC SPEED OF THE WARNING SEQUENCE LED CREW TO SUSPECT VALIDITY OF WARNING. THIS INCIDENT OCCURRED IN IMC CONDITIONS & WAS BELIEVED AT THE TIME TO BE A NEAR MISS. THE TCAS AND TRANSPONDER COMPUTERS WERE REPLACED AND ARE BEING EVALUATED.