BEECH C23 PLT ENTERED TEB CLASS D AIRSPACE WHILE ATTEMPTING TO CONTACT THE TWR FOR LNDG INSTRUCTIONS.

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NEW YORK APCH INSTRUCTED ME TO DSND FROM 3500 FT TO TEB PATTERN ALT; APPROX 15 MI W OF TEB. I DID SO AND REACHING 1500 FT; I ADVISED NEW YORK. THEY ACKNOWLEDGED AND APPROX 5-6 MI FROM TEB ARPT; THEY INSTRUCTED ME TO CONTACT TEB TWR ON 119.5. MY COPLT DID SO AND WAS TOLD TO 'REMAIN CLR OF TEB CLASS D AIRSPACE AND RETURN TO NEW YORK APCH FREQ.' WE WERE AT 1500 FT AND STILL ABOUT 5 MI FROM TEB. I THOUGHT WE WERE STILL CTLR OF TEB CLASS D AIRSPACE AS WE WERE 5 MI OUT. I CONTINUED FOR A FEW MORE SECONDS WHILE MY COPLT TRIED TO CONTACT NEW YORK. SHE WAS UNSUCCESSFUL BECAUSE OF FREQ CONGESTION. TEB TWR CALLED AGAIN AND SAID WE WERE INSTRUCTED TO REMAIN CLR OF CLASS D AIRSPACE AND THAT WE WERE NOW 'WELL WITHIN IT.' HE INSTRUCTED ME TO MAKE AN IMMEDIATE TURN TO 360 DEGS. I COMPLIED IMMEDIATELY AND APOLOGIZED. HE THEN VECTORED US FOR THE VISUAL TO RWY 6. WE FLEW THE APCH AND LNDG WITHOUT FURTHER INCIDENT. CONTRIBUTING FACTORS: 1) NEW YORK APCH HAVING US DSND TO PATTERN ALT AND THEN TURNING US OVER TO TEB TWR ONLY 5 MI OUT. 2) TFC CONGESTION AT TEB. 3) TWR INSTRUCTING US TO RETURN TO NEW YORK APCH AND INABILITY TO DO SO BECAUSE OF FREQ CONGESTION. 4) MY MISUNDERSTANDING AS TO WHERE CLASS D AIRSPACE STARTED OR TWR'S MISINTERP.