BEECH V35 PLT HAS AN NMAC DURING APCH TO LGB.

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V35A XXX WAS APPROX 13 NM W OF LGB AT 3000 FT MSL; SQUAWKING 1200. XXX MADE INITIAL CONTACT WITH LGB TWR (119.4) REQUESTING LNDG CLRNC FOR RWY 25L; WITH TXWY K. LGB TWR CLRED XXX FOR DIRECT ENTRY TO DOWNWIND FOR RWY 25L AND TO RPT XING THE 710 FREEWAY. ACKNOWLEDGED TWR CLRNC AND REPEATED INSTRUCTIONS FOR DOWNWIND ENTRY FOR RWY 25L AND TO RPT XING THE 710 FREEWAY. I THEN STARTED A GRADUAL DSCNT FOR THE PATTERN AT LGB. LGB TWR ADVISED XXX AT THIS POINT OF A CESSNA STATIONAIRE DEPARTING RWY 25L; TURNING TO 180 DEGS AFTER 800 FT. RPTED XING THE 710 FREEWAY AND ADVISED LGB TWR THAT I DIDN'T HAVE VISUAL CONTACT WITH THE CESSNA DEPARTING RWY 25L. 10 OR 15 SECONDS LATER I WAS AT 1600 FT MSL AND 130 KTS. I AGAIN ADVISED LGB TWR THAT I HAD NO VISUAL CONTACT WITH THE CESSNA. BECAUSE OF THE LACK OF VISUAL CONTACT; I STOPPED MY DSCNT. I AM CONVINCED THIS PREVENTED A MIDAIR COLLISION; BECAUSE SECONDS LATER I SAW THE CESSNA DIRECTLY BELOW AND SLIGHTLY TO THE L OF MY ACFT. THE CESSNA WAS IN A CLBING L TURN 100-150 FT BELOW MY POS. OUR CONVERGING COURSES PUT US IN EXTREME DANGER OF A MIDAIR COLLISION. ONLY OUR ALT SEPARATION PREVENTED PHYSICAL CONTACT. NOTE: I DON'T KNOW IF THE CESSNA EVER SAW XXX. I ALSO DON'T KNOW IF THE CESSNA WAS MADE AWARE OF XXX APCH TO THE PATTERN FROM THE DOWNWIND POS. I WOULD GUESS THE CESSNA HAD SWITCHED TO DEP FREQ AND DIDN'T MONITOR MY CALLS TO LGB TWR ADVISING OF MY LACK OF VISUAL CONTACT WITH THE CESSNA. AT THIS POINT I THINK I RPTED TO LGB TWR THAT XXX HAD VISUAL CONTACT WITH THE CESSNA. I ALSO SAID SOMETHING TO LGB TWR ABOUT NOT GIVING XXX TFC AVOIDANCE TURNS TO HELP MEDIATE POSSIBLE CONFLICTS. LGB TWR RESPONDED TO XXX DEFENSIVELY; SAYING THE CESSNA WAS IFR AND THAT XXX SHOULD HAVE ALTERED COURSE TOWARD THE CTR OF THE ARPT OF MY OWN VOLITION IF I DIDN'T HAVE VISUAL CONTACT WITH THE CESSNA. XXX CONTINUED DSCNT AND LANDED ON RWY 25L. AT THIS POINT I WAS ANGRY WITH MYSELF FOR NOT SEEING THE CESSNA UNTIL IT WAS ALMOST TOO LATE FOR EVASIVE ACTION.