WHILE ON A FLT FOR THE PURPOSE OF GIVING SEVERAL FOREIGN PLTS EXPERIENCE IN JET ACFT; A TRAINING PLT INITIATED A CLB IN CLASS A AIRSPACE WITHOUT AN ATC CLRNC. ARTCC RADAR CTLR INTERVENED. INSTRUCTOR PLT HAD BEEN PROGRAMMING THE GPS AND FAILED TO NOTICE THE EXCURSION UNTIL AFTER THE ACFT HAD CLBED 1000 FT. ALTDEV EXCURSION FROM ASSIGNED.

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THIS WAS A FLT TO GIVE SEVERAL FOREIGN PLTS EXPERIENCE IN JET ACFT. THE TRAINING PLT WAS FROM A FLT TRAINING ACADEMY IN CALIFORNIA. OUR COMPANY LEASED THE LEARJET TO THIS ACADEMY FOR TRAINING. DUE TO SCHEDULING PROBS; I WAS ASKED TO FLY WITH THESE PLTS FOR THEIR LAST SEVERAL FLTS BEFORE GRADUATION. MY FIRST TIME FLYING WITH THEM IS WHEN THIS OCCURRED. WE WERE LEVEL AT FL270 FOR ABOUT 10 MINS. ATC THEN CLRED US DIRECT TO LIDAT INTXN. I RESPONDED AND PROCEEDED TO SHOW THE TRAINING PLT. I THEN BEGAN TO ENTER THE WAYPOINT IN THE GPS. UP TO THIS TIME THE PLT WAS DOING A GOOD JOB HOLDING ALT. WHEN I LOOKED DOWN; THE FOREIGN PLT PUT FL370 IN THE ALERTER AND PULLED BACK TO CLB TO FL370. ABOUT FL280 I LOOKED UP JUST AS ATC WAS CALLING. I HAVE NO IDEA WHAT THIS STUDENT WAS THINKING. I IMMEDIATELY GRABBED THE ACFT; PUT OUT THE SPOILERS; AND GOT BACK TO FL270. SOMEHOW; HE DECIDED WE WERE CLRED TO FL370; EVEN THOUGH THERE WAS NO CONVERSATION REGARDING CHANGING ALT. AFTER THIS INCIDENT; I REALIZED THESE PLTS DON'T HAVE THE REAL PICTURE OF WHAT'S GOING ON UP THERE. I BASICALLY LET THEM MONITOR THE AUTOPLT. ALSO; SINCE HE CHANGED THE ALERTER; AFTER BEING TOLD NOT TO TOUCH THE ALERTER; THE BELL DID NOT RING A 300 FT DEV TO WARN ME.