A PA28 NBOUND ABEAM OMN HAS A SERIOUS NMAC WITH AN ACFT THAT WAS ON CTAF ON APCH SBOUND.

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ON UPWIND OF RWY 35 AT ORMOND BEACH MUNICIPAL ARPT; I HEARD ANOTHER ACFT OVER THE CTAF STATING THAT HE WAS N OF ORMOND HEADING S FOR AN APCH. I ADVISED THE TFC OF MY POS AND ASKED HIM IF HE WOULD LIKE ME TO DIVERT AWAY TO GIVE HIM SOME ROOM. HE DECLINED MY OFFER STATING THAT HE HAD ME IN SIGHT AND WOULD BE GOING MISSED. I ADVISED HIM WE WOULD BE CLBING N AND THEN; UPON REACHING OUR DESIRED ALT; WOULD CALL DAYTONA ATC AND WOULD BE HEADING S WITH THEM. HE ACKNOWLEDGED THIS. BEING THAT HE HAD ME IN SIGHT; I ASSUMED HE WOULD AVOID US. I DID NOT CHANGE MY DIRECTION; BUT DID START TO CLB; AS I HAD TOLD HIM I WOULD; AFTER BECOMING CLR OF DAYTONA INTL'S AIRSPACE. A FEW MINS LATER; I BECAME AWARE OF THE FACT THAT THE ACFT HAD BANKED DRASTICALLY INTO OUR DIRECTION; WAS IN A RAPID DSCNT; AND WAS SECONDS AWAY FROM COLLIDING WITH MY ACFT. MY REACTION; AS APPROPRIATE; WAS TO DIVE AWAY FROM HIM. THE OTHER ACFT WAS SO CLOSE THAT I WAS CERTAIN HE WAS GOING TO; AT THE VERY LEAST; CLIP MY TAIL. LUCKILY; I WAS UNSCATHED ALTHOUGH CONSIDERABLY SHAKEN. AT THAT POINT THE ACFT CONTACTED ME ON ORMOND BEACH'S CTAF AND ASKED ME TO CONTACT DAYTONA. I DID SO AND FROM THAT POINT ON THE FLT WAS; RELATIVELY; UNEVENTFUL. THE ONLY WAY THIS COULD HAVE BEEN AVOIDED WOULD HAVE BEEN FOR THE ACFT THAT NEARLY HIT ME TO HAVE BEEN MORE AWARE OF HIS SURROUNDINGS AND TO HAVE KEPT A THOROUGH SCAN UP. IT WAS ESPECIALLY APPARENT THAT HE WAS NOT PAYING ATTN TO HIS SURROUNDINGS SINCE HE TURNED DIRECTLY IN TOWARD ME AND; AS FAR AS I COULD TELL BEFORE I DOVE AWAY; MADE NO ATTEMPT TO AVOID COLLISION.