PLT OF A C172 MADE A 360 DEG TURN IN THE OPPOSITE DIRECTION OF A PIPER SARATOGA; PA32; ON FINAL FOR THE SAME RWY AT AN UNCTLED ARPT FOR ADEQUATE SPACING.

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ON THE MORNING OF SEP/XA/99; I DEPARTED LAKE IN THE HILLS ARPT (3CK) AND FLEW TOWARDS SCHAUMBURG ARPT (06C); MONITORED UHF 123.0 AND CONFIRMED THAT RWY 11 WAS THE ACTIVE. I FLEW SE TO THE INTXN OF I-90 AND BARRINGTON ROAD BY WHICH TIME I HAD DSNDED TO BTWN 1700-1800 FT MSL TO CONTINUE UNDER THE FLOOR OF THE CLASS B AIRSPACE. AFTER THAT; I HEARD A CESSNA SAY THAT HE WOULD BE ENTERING DOWNWIND FOR RWY 11. I CONTINUED SE WHILE LOOKING FOR THE CESSNA. EVENTUALLY I SAW A CESSNA E OF THE ARPT ABOVE MY ALT AND HDG IN MY DIRECTION. 'HE IS ABOVE THE FLOOR OF CLASS B AIRSPACE' FLASHED THROUGH MY MIND. I DID NOT CONSIDER HIM TO BE MY CESSNA TFC. ABOUT THEN; A SARATOGA CALLED A FEW MI S FOR RWY 11. I TURNED TO A HDG OF ABOUT 110 DEGS FAR ENOUGH NW OF THE RWY TO BE N OF TFC ON DOWNWIND AND CONTINUED LOOKING FOR THE CESSNA THAT HAD CALLED ENTERING DOWNWIND. I GOT ALMOST TO A POINT DIRECTLY N OF THE ARPT BEFORE I SAW A CESSNA TO MY R ON MIDFIELD DOWNWIND. I THEN CALLED MY DOWNWIND ENTRY AND TURNED R 180 DEGS TO FOLLOW HIM. THE CESSNA TURNED A NORMAL L BASE FOR RWY 11. THEN THE SARATOGA CALLED FOR A R BASE ENTRY TO RWY 11. THE CESSNA TURNED FINAL AND THE SARATOGA MADE A R TURN TO FINAL BEHIND HIM. I TURNED A L BASE AFTER THE SARATOGA PASSED OFF MY L WING ON FINAL. JUST AS I FINISHED MY TURN TO L BASE; THE SARATOGA STARTED A R 360 DEG TURN BECAUSE HE WAS TOO CLOSE BEHIND THE SLOWER CESSNA. I IMMEDIATELY STARTED A L 360 DEG TURN AND ANNOUNCED '...DOING A L 360 DEG TURN FROM A L BASE TO ALLOW THE SARATOGA TO LAND' SO THAT HE WOULD KNOW WHAT I WAS DOING RELATIVE TO HIM. IF I HAD CONTINUED; HE WOULD PROBABLY HAVE ROLLED OUT ON FINAL AS I TURNED ON FINAL! HE SAID THANKS AND LANDED; TURNING OFF NEAR THE FAR END OF THE RWY. I LANDED SHORTER; TURNED OFF NEAR MID-FIELD; AND HELD SHORT OF THE PARALLEL TXWY UNTIL HE TAXIED BACK PAST ME.