(Reuters) - U.S. carrier Alaska Airlines said on Thursday it will buy 50 737 single-aisle jetliners, worth $5 billion at list prices, from Boeing Co in its largest order yet.

The order includes 37 of Boeing's upcoming 737 MAX, the new-engine variant of the popular 737 that offers better fuel efficiency. Alaska is also taking 13 Next-Generation extended-range 737 jets.

Alaska Airlines, whose parent is Alaska Air Group Inc , currently operates an all-Boeing fleet of 120 737s, and signaled in a statement that it intends to have only Boeing jets for many years. It said the newest planes, most of which will replace older aircraft, are to be delivered between 2015 and 2022.

The 737 MAX is Boeing's answer to the Airbus A320neo jet, a revamp of the A320 family that will have more efficient engines. Airbus, a unit of Europe's EADS , and Boeing compete for the lion's share of a jet market estimated at $100 billion a year.

Earlier this month, Boeing reported an increase in orders for its third quarter, helped by the MAX.

It said the Alaska Airlines order brought the total number of MAX orders to 858 to date.

Boeing's shares were up 1.1 percent to $71.10 in morning trading, while Alaska Air was down 0.2 percent to $36.51.

(Reporting by Neha Alawadhi and A. Ananthalakshmi in Bangalore and Karen Jacobs; Editing by Sreejiraj Eluvangal and Gerald E. McCormick)