MD80 FLT CREW HAS UNCOMMANDED CLB WHILE AT FL310 IN CRUISE. FLT CREW DISCONNECTS AUTOPLT AND DSND TO A LOWER ALT.

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WHILE IN CRUISE THE AUTOPLT SUDDENLY STARTED A CLB; THE FO DISCONNECTED THE AUTOPLT AND PUSHED THE NOSE OVER TO RETURN TO OUR ALT. IT TOOK A FEW SECONDS TO GET THE AIRPLANE BACK TO OUR ASSIGNED ALT DUE TO THE UNUSUALLY HIGH STABILIZER SETTING THE AUTOPLT HAD SET. AT THE SAME TIME; I NOTICED THAT DUE TO THIS PROB OUR AIRSPD HAD DECREASED AND THAT THE THROTTLES WERE HAVING TROUBLE ACCELERATING THE AIRPLANE; WE HAD BEEN SWITCHED OVER TO ZLC AT THIS TIME SO I REQUESTED FL290; IN DOING SO WE WERE ABLE TO GET OUR SPD BACK. ONCE LEVEL WE ATTEMPTED TO RE-ENGAGE BOTH AUTOPLTS; BOTH CONTINUED TO WANT TO CLB. WE ELECTED TO CONTINUE THE FLT WITHOUT AUTOPLTS AND LANDED DFW WITH NO FURTHER PROBS. EDMONTON GAVE NO INDICATION THAT THERE WERE ANY PROBS WITH OUR ALT CHANGE WHICH WAS APPROX 350-400 FT HIGH BY THE TIME WE WERE ABLE TO GET UNDER CTL. SUPPLEMENTAL INFO FROM ACN 694005: WE DECIDED THAT THE AIRPLANE WAS PERFECTLY CTLABLE WITH THE AUTOPLT OFF; SO WE CONTINUED THE FLT TO DFW. DURING THE INITIAL UNCOMMANDED CLB; HOWEVER; WE HAD A SLIGHT ALTDEV FOR A FEW SECONDS. ATC DID NOT SAY ANYTHING ABOUT THE ALTDEV.