NEW YORK – CenturyTel Inc., the country’s fifth-largest local phone company, plans to buy the third-largest, Qwest Communications International Inc., in a stock deal worth more than $10 billion so the companies can try to better deal with the dark future of the landline phone business.

The number of landline phone users in the U.S. shrinks by about 10 percent per year as consumers increasingly rely on their wireless phones or service from cable companies. That means a major challenge for phone companies is cutting their costs to keep pace with their dwindling business.

Buying Qwest could give CenturyTel a chance to cut overlapping functions like billing, administration, call centers and back-end services, eliminating jobs in the process.

In a sense, the deal is a way to return to the scale that phone companies had before wireless started eviscerating the business. If they combined today, CenturyTel and Qwest would have the same number of phone lines that Qwest did on its own eight years ago.

The combined company would have about 17 million phone lines serving customers in 37 states. It would be based at CenturyTel’s headquarters in Monroe, La., rather than in Denver, where Qwest is based.

One big hurdle for the new company would be that neither Qwest nor CenturyTel own wireless networks that can compensate for the loss of landlines, as AT&T Inc. and Verizon Communications Inc. do. Last year, 22.7 percent of homes used only cell phones, according to a survey by the Centers for Disease Control and Prevention.

Qwest and CenturyTel hope the acquisition can make the combined company better able to weather the future. Qwest has a large and stable business selling telecommunications services to business and government customers. Together, the companies would be the fifth-largest residential Internet service provider in the country, and both have been upgrading their networks to provide higher speeds, though they are not able to match the latest round of upgrades at cable companies.

Glen Post, the CEO of CenturyTel, said the combined company may also provide TV services over phone lines to compete more aggressively with cable. CenturyTel has started providing TV services on a small scale in some areas. Post would be the CEO of the new company.

Qwest provides traditional phone service in 14 mostly Western states.