INSTR WITH SPI AT NON TWR ARPT HAS TWIN ACFT CUT IN ON BASE TURN AND LAND AHEAD. REMAINS IN PATTERN AND DEPARTS DIRECTLY BEHIND INSTR ACFT.

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I WAS GIVING INSTRUCTION FOR 61.31 TAIL WHEEL TRANSITION. IN THE PATTERN DOING TOUCH AND GOES WE WERE ABEAM THE APCH END OF RWY 33 IN A R HAND TFC PATTERN AFTER HAVING CALLED DOWNWIND FOR TOUCH AND GO. MIDFIELD DOWNWIND 2 PEOPLE IN A GREEN ON WHITE SMA RPTED ON A R DOWNWIND FOR 33 AND GOING FASTER THAN US. THEY CAME STRAIGHT AT US; VERY CLOSE AND CUT INSIDE OF US FROM BEHIND AND ENTERED A VERY CLOSE IN R BASE. THIS ACFT SHOWED INTENT. WE LANDED BEHIND THEM AND BOTH STAYED IN THE PATTERN. THEY TALKED TO UNICOM AND GOT AN ADVISORY BUT WOULD NOT RESPOND TO US. NEXT; WE WERE ON SHORT FINAL FOR THE 33R GRASS AND CALLED TURNING FINAL AND SMA RPTS DEPARTING RWY 33 HE TAXIES OUT AS WE WERE LNDG AND TAKES OFF R BEHIND US BECAUSE WE ARE REQUIRED TO ANGLE OVER TO RWY 33 TO CLR BUILDINGS AND ACFT. THE SMA IS VERY CLOSE RIGHT BEHIND US. MY STUDENT IS NERVOUS. WE STARTED TO TURN TO THE L (W) TO ALLOW THEM TO PASS AND THEY STEERED L TOWARDS US AS IF TO PASS ON THE L. THEN WE DEPARTED TO H10 TO THE S. THEY DEPARTED TO THE N. THE RADIO CALLS HAD AN ACCENT SOMEWHAT (ENGLISH).