What was found
WHILE CLIMBING AROUND FL300 TO FL400 THE RIGHT ENGINE SPOOLED DOWN TO APPROX 84% AND THE IGNITION CAME ON. THE MCT LIGHT WENT AWAY AND THE FUEL FLOW WAS REDUCED ON THE RIGHT ENGINE AS WELL. IT DID IT AGAIN LESS THAN A MINUTE LATER. WE LEVELED AT FL350 AND IT HAD REOCCURRED SEVERAL MORE TIMES DURING THE CLIMB. AT LEVEL OFF WHEN THE THRUST LEVERS WERE PULLED BACK THE PROBLEM CONTINUED. THROUGHOUT THE FIRST PART OF OUR DECENT THE ISSUE CONTINUED. WE HAD DECLARED AN EMERGENCY TO RSW AND THEN CHANGED THE DESTINATION TO APF. AT SOME POINT IN THE DECENT THE PROBLEM STOPPED AND WE LANDED WITHOUT INCIDENCE.