Notably, American Airlines, which operates one of the largest fleets of planes in the world, does not even serve peanuts. But it does have a peanut policy, in which it states: “Requests that we not serve any particular foods, including tree nuts, on our flights cannot be granted. We are not able to provide nut ‘buffer zones,’ nor are we able to allow passengers to pre-board to wipe down seats and tray tables.”

“Ultimately we cannot guarantee customers will not be exposed to peanuts or other nuts during the flight, and allowing people with nut allergies to preboard can create a false sense of security and does not eliminate risk,” Mr. Miller said.

Individuals who suffer from severe, life-threatening food allergies can experience swelling and difficulty breathing after even a mild exposure. They usually carry an Epi-Pen, which contains epinephrine, a medication that can reverse the symptoms. But in the case of a severe reaction, a person may still need urgent access to a medical facility.

Research has shown that taking steps like creating buffer zones, in which nearby passengers are asked to refrain from eating nut products, and wiping down seats and trays may reduce the risk of an allergic reaction in flight.

One of the complaints, filed on Dec. 28, is from Nicole Mackenzie, the mother of a 7-year-old with life-threatening allergies to peanuts, tree nuts and seeds. She was not allowed to preboard to clean the seat before the family’s trip last fall from Portland, Ore., to Charlotte, N.C. The second complaint was filed on Jan. 10 on behalf of Food Allergy Research & Education (FARE), an organization that represents individuals with all kinds of food allergies.

“American Airlines’s action was clearly discriminatory,” said FARE’s chief executive officer and chief medical officer, Dr. James Baker Jr. “It has a defined policy that they put on their website, and the only people they single out from preboarding are people with food allergies.”

Lianne Mandelbaum, whose son has allergies, tracks the experiences of travelers with allergies on her website, the No Nut Traveler. She said that each airline makes its own rules but that the policies are inconsistently enforced, so travelers often don’t know what to expect when they make travel plans.