TWO FLIGHT INSTRUCTORS TRY TO USE THE SAME AIRSPACE FOR PRACTICE MANEUVERS. AFTER PASSING WITHIN A HALF A MILE OF EACH OTHER ONE INSTRUCTOR DECIDES TO LEAVE THE AREA.

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WHEN ENTERING INTO UNUSUAL FLT ATTITUDES FOR A BEGINNING INST STUDENT WE XMITTED OUR POS; ALT AND INTENTIONS OVER THE COMMON PRACTICE AREA FREQ AND HEARD A PIPER ARROW STATE THAT THEY WERE OVER THE SAME REF AT ROUGHLY THE SAME ALT. AT THIS TIME I TOLD MY STUDENT WHO WAS WEARING A VIEW LIMITING DEVICE TO HELP ME LOOK FOR THE OTHER TFC. AFTER SEARCHING FOR AND CONFIRMING THE POS OF THE OTHER AIRPLANE WE DECIDED TO DEPART TO THE W TO AVOID THE AREA. AS SOON AS WE ROLLED WINGS LEVEL; I SAW THE TFC BELOW US BY ABOUT 300-500 FT AND LESS THAN 1/2 SM HORIZ. I IMMEDIATELY ROLLED AWAY FROM THE TFC AND OBSERVED THEM ENTER INTO WHAT I THOUGHT WAS AN EVASIVE TURN OF THEIR OWN; HOWEVER; IT APPEARED THEY HAD ENTERED INTO A STEEP TURN. I ASKED THE PLT OF THE OTHER AIRPLANE IF SHE WAS LOOKING FOR US AND SHE REPLIED 'NO WE HAS YOU IN SIGHT;' HOWEVER; IN MY OPINION THAT IS NOT A PROPER RESPONSE. AFTER RECEIVING THAT ANSWER; MY STUDENT AND I BOTH DECIDED TO RETURN TO THE ARPT. SUPPLEMENTAL INFO FROM ACN 728223: AFTER COMPLETING CLRING TURNS IN PREPARATION FOR A SERIES OF INST STEEP TURNS WE OBSERVED A PIPER ARROW FLYING FROM OUR L TO R ABOUT 300 FT ABOVE US AND LESS THAN 1 MI HORIZ. WE COULD CLRLY SEE THE TAIL MARKINGS AND THAT THE AIRPLANE WAS A PIPER ARROW. WE WERE MAKING ALL NECESSARY PRACTICE AREA POS RPTS AND HAD HEARD NOTHING FROM THE OTHER AIRPLANE EITHER BEFORE OR AFTER OUR NEAR MISS.