NEW YORK - Air China, the nation’s biggest carrier by market value, agreed to buy two Boeing 747-8 aircraft in the planemaker’s first sale of the models this year.

The airline also will purchase one wide-body 777-300 plane, 20 single-aisle 737-800 jets and eight 777 freighters, according to a statement. The planes have a combined catalogue value of $4.8 billion and Boeing granted “significant price concessions” through credit agreements, the airline said in the statement.

Boeing, based in Chicago, hasn’t sold more than five 747-8 aircraft a year since Deutsche Lufthansa purchased 19 of the planes in 2006, and concern that persistently weak demand could prompt the company to curtail production has been mounting. The orders may help alleviate some of the pressure, according to Stephen Levenson of Stifel Financial.