You need to find out a few details first.
If the patient is the subscriber of both plans; the plan that has been effective the longest is primary. You will need to send eligiblity reports showing the carrier who has been effective longer both eligiblity reports.
If the patient is the subscriber on one and a spouse is the subscriber on the other, the person who's birthday comes first in the month and day is primary according to the birthday rule. You will need to send a letter showing the primary carrier and a letter attesting to the fact.
Good luck this can become extremely frustrating at times!