SMA WITH INSTRUCTOR AND SPI CROSSES ACTIVE RWY WITHOUT CLRNC.

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IT WAS NOV/SUN/92 APPROX XX30 PM WHEN MY STUDENT AND I TAXIED FROM THE RAMP ON THE N SIDE OF BRACKETT ARPT IN SMA X. OUR INTENTION WAS TO TAXI TO THE FUEL STATION ON THE S SIDE OF THE ARPT. ON OUR WAY TO THE FUEL STATION WE HAVE TO CROSS BOTH RWYS 26R AND 26L AT TAXIWAY ECHO (SEE PICTURE). BEFORE DEPARTING THE RAMP ON THE N SIDE; MY STUDENT CALLED BRACKETT GND CTL REQUESTING TO TAXI TO FUEL. GND CTL RESPONDED SMA X TAXI TO FUEL; HOLD SHORT OF RWY 26R AT ECHO.' AFTER ACKNOWLEDGING THIS XMISSION PROCEEDED AND HELD SHORT AT RWY 26R AT ECHO WHERE THE GND CTLR ASKED US TO STANDBY. AT THIS TIME; ANOTHER SMA Y ALSO COMING FROM THE N RAMP WITH THE SAME INTENTIONS HELD IN SEQUENCE BEHIND US. THE GND CTLR GAVE THE FOLLOWING INSTRUCTIONS TO SMA Y 'YOU WILL BE FOLLOWING SMA X TO FUEL.' THIS XMISSION WAS MISUNDERSTOOD BY MY STUDENT WHO HEARD HIS TAIL NUMBER AND THOUGHT WE NOW HAD PERMISSION TO CROSS RWY 26R AND ACKNOWLEDGED WITH SMA X. AT THIS POINT MY STUDENT STARTED TAXIING. I DID NOT REALIZE EXPECT HIS REACTION. BECAUSE I WAS DISTRACTED FOR A MOMENT; BY THE TIME I REALIZED WE WERE MOVING; WE WERE ON THE RWY ALREADY TOO FAR. THE ONLY SAFE CHOICE WAS TO CONTINUE ACROSS AND CLR THE RWY AS QUICKLY AS POSSIBLE. JUST BEFORE THIS HAPPENED; AN ACFT HAD LANDED ON RWY 26R AND WAS ROLLING TO A STOP. THERE WAS NO IMMEDIATE DANGER BECAUSE THE ACFT THAT HAD JUST LANDED WAS ALREADY SLOWING TO A STOP AND WE WERE AT NO TIME CLOSER THAN 1000 FT.