NMAC BTWN A C340 IN A STEEP TURN AND DSNDING XING TFC; A BONANZA.

Narrative

I WAS ACTING AS INSTRUCTOR DURING A FLT REVUE IN THE CUSTOMER'S OWN C340. HE PROCEEDED TO ATTEMPT A R-HAND 45 DEG BANK; 360 DEG TURN. THE FIRST ATTEMPT WAS ABORTED DUE TO INCORRECT ROLL-IN. THE SECOND ATTEMPT WAS COMPLETED. THE NEXT TURN WAS A L-HAND 45 DEG BANK; 360 DEG TURN. WE WERE TURNING THROUGH APPROX A 360 DEG HEADING. APPROX 30 DEGS PRIOR TO ROLLOUT; I NOTICED A BE33 OR BE36 PASSING APPROX 200-300 FT BENEATH US. WE WERE ON A SOUTHERLY HEADING. THE ACFT PASSING BENEATH US WAS PASSING L TO R ON A WESTERLY HEADING. AS I FIRST NOTICED THE ACFT AS IT WAS PASSING BENEATH US; NO EVASIVE ACTION WAS TAKEN ON OUR PART. UPON APCH TO LGB; WE WERE ASKED TO CALL SOCAL APCH CTL AFTER LNDG. AFTER CALLING SOCAL; I LEARNED THAT THE PLT OF THE OTHER ACFT HAD FILED A NEAR MISS RPT. THE PLT HAD STATED THAT HE HAD PASSED BENEATH US; AND WE ABOVE HIM; 2 OR 3 TIMES WHILE ON APCH TO TOA. UNLESS HE WAS THE ACFT THAT PASSED ABOVE US; WE ONLY HAD HIM IN SIGHT AT ONE TIME. CONTRIBUTING FACTORS TO OUR LATE DISCOVERY OF THE OTHER ACFT COULD BE THE LIMITED VISIBILITY IN THE DIRECTION OF TURN IN THE C340; ESPECIALLY FROM THE SEAT OPPOSITE DIRECTION OF TURN. IF THE PLT OF THE OTHER ACFT HAD US IN SIGHT; I DO NOT KNOW WHY (OR IF) HE STAYED ON A COURSE AND ALT THAT WOULD CAUSE QUESTIONABLE SEPARATION. ONE POSSIBILITY WOULD BE THAT OUR FAIRLY STEEP TURN WAS NOT ANTICIPATED BY THE PLT.