What was found
DURING CLIMB, PASSING FL340, RECEIVED A RED AUTO SLATS FAIL CAS MESSAGE SAME TIME THE STICK SHAKER WENT OFF. DISENGAGED AUTOPILOT & LEVELED OFF TO INCREASE AIRSPEED. TLA’S SET IN CLIMB POWER DETENT. STICK SHAKER REMAINED ON & AOA INDICATOR SHOWING .2. THROUGHOUT THE EVENT THE CO-PILOT REPORTED THE RED AUTO SLATS FAIL CAS MESSAGE OCCURRED ANOTHER 3-4 TIMES. NOTICED AN AMBER SLATS FAIL CAS MESSAGE INTERMITTENT. AND A WHITE/AMBER SPEED TAPE FLUCTUATING UP AND DOWN. ALL AIRSPEED INDICATIONS APPEARED NORMAL. STICK SHAKER CONTINUED FOR SEVERAL MINUTES. AFTER LEVEL OFF AT APPROX FL363, & EMERGENCY INDICATIONS STILL PRESENT, RECEIVED A CLEARANCE TO FL350 & BEGAN DESCENT. DURING DESCENT, STICK SHAKER PERSISTED. LEVELED AT FL350, & IT WAS EXTREMELY DIFFICULT TO MAINTAIN ALTITUDE WITH THE STICK SHAKER ACTIVE. STATED OUR INTENTIONS AND DECLARED AN EMERGENCY. STICK SHAKER CONTINUED FOR ANOTHER SEVERAL THOUSAND FT, THEN STOPPED. DURING THE DESCENT, STICK SHAKER CAME ON 2 MORE TIMES. STICK SHAKER STOPPED FOR FINAL TIME ON DESCENT THROUGH APPROX 17,000 FT. NO MORE ABNORMAL INDICATIONS AND WE LANDED WITH NO OTHER INCIDENT. MAINTENANCE REPLACED THE AOA COMPUTER AND AOA PROBE AND THE SYSTEM OPERATIONALLY CHECKED NORMAL.