NEW YORK — With the exception of Southwest Airlines, several of the nation's largest carriers reported significant declines in passenger demand during December, compared with the previous year.

        American Airlines, America West Airlines and Continental Airlines each reported double-digit percentage declines for the month, although their data provide evidence that demand for air travel improved on a month-to-month basis.

        Shares of most major carriers rose Friday after investors saw further evidence that passenger demand, while weak, is gradually improving.

        Southwest, based in Dallas, said Friday that traffic grew by about 0.6 percent to 3.55 billion revenue passenger miles, a measure of the number of paying customers that travel one mile. Southwest bucked another industry trend by increasing capacity, or the number of available seats, by 3 percent.

        American, the nation's largest carrier, said Friday that traffic decreased 17.4 percent from a year ago and that capacity was 15 percent lower. The Fort Worth, Texas-based carrier reported 9.08 billion revenue passenger miles.

        America West of Phoenix said late Thursday that December traffic fell 15 percent to 1.34 billion revenue passenger miles, while capacity was 14 percent below year ago levels.

        Houston-based Continental, which also announced its results for December on Thursday, said traffic slipped by 10 percent to 4.5 billion revenue passenger miles and that capacity was off by 12 percent.

        In November, industrywide passenger demand was down 20 percent from the previous year, according to the Air Transport Association, an industry group that compiles data from the nation's largest carriers.

        Shares of AMR Corp., the parent company of American, rose $1.36, or nearly 6 percent, to $25 on the New York Stock Exchange, where those of Continental gained $1.26, or 4 percent, to $31.30. Shares of Southwest rose a nickel to $18.96 on the NYSE.

        America West's stock declined 19 cents to $4.55 on the NYSE as analysts believe the carrier is in worse financial shape than its competitors.

        Other airlines were expected to announce their results for the month over the next few days.

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