A federal appeals court will soon hear oral arguments in lawsuits brought by citizens of Vietnam and American Vietnam War veterans who say their health has suffered from exposure to the defoliant Agent Orange.

The appeals are being brought under a variety of legal theories, and the court could arrive at opposite conclusions about whether the Vietnamese or American plaintiffs may go forward with their claims against the chemical companies that manufactured Agent Orange.

The arguments are set for June 18 before the U.S. 2nd Circuit Court of Appeals in Manhattan. They represent the latest round of Agent Orange litigation in a series of battles that have spanned nearly three decades. In 1984, several producers of the defoliant agreed to pay $180 million to settle a class action suit brought by American veterans. But that money has long since been paid out, and veterans who were not part of that suit say their symptoms only became apparent in recent years.

Agent Orange contains the most toxic form of the compound dioxin. The defendants, which include Dow Chemical Company, Monsanto Company, and Hercules Incorporated, dispute allegations that Agent Orange is the cause of cancers, birth defects, and other illnesses in the plaintiffs...