WAKE TURB ENCOUNTERED BY A CLBING MD80 BEHIND AND BELOW A PRECEDING B737 ON FREQ WITH ZOB.

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WE WERE STEP CLBING FROM FL310 TO FL350 IN SMOOTH AIR WITH NO RPTED TURB ALONG OUR RTE. WE WERE 10 MI IN TRAIL OF ANOTHER ACFT AT FL350. WHILE CLBING AT MACH .76; AT APPROX FL346 WE ENCOUNTERED MODERATE TURB WITH A NOTICEABLE ROLLING MOTION. THE PROGRESS OF OUR CLB STOPPED; THE INDICATED MACH FLUCTUATED +/-.10 MACH. THE FO; WHO WAS FLYING THE AIRPLANE; DISCONNECTED THE AUTOPLT IN AN ATTEMPT TO CTL THE ACFT AND CLB THROUGH THE TURB. I TURNED ON THE SEAT BELT SIGN AND MADE A PA FOR THE FLT ATTENDANTS TO IMMEDIATELY TAKE THEIR SEATS. THE CLB CONTINUED TO STAGNATE AND THE TURB CONTINUED AS OUR MACH DECREASED. WE INFORMED ATC THAT WE HAD FLOWN INTO AN ENCOUNTER WITH MODERATE TURB AND THAT WE WERE DSNDING. ATC CLRED US BACK TO FL310. THE TURB STOPPED AS WE DSNDED THROUGH APPROX FL344. WE CONTINUED THE DSCNT TO FL310 IN SMOOTH AIR. I CALLED THE FLT ATTENDANTS TO CHK ON THE SIT IN THE CABIN AND FOR ANY POSSIBLE INJURIES. THERE WERE NO INJURIES RPTED AND THE CABIN WAS SECURE. LEVEL AT FL310; I RELEASED THE FLT ATTENDANTS AND TURNED THE SEAT BELT SIGN OFF. WE INFORMED ATC THAT WE THOUGHT WE HAD EXPERIENCED A WAKE TURB ENCOUNTER. WE ASKED ATC WHAT TYPE OF ACFT WE WERE FOLLOWING AND WERE TOLD IT WAS A 500 SERIES B737. I WAS SURPRISED; EXPECTING TO LEARN THAT THE PROCEEDING ACFT WAS A WBD OF SOME SORT.