Perhaps to the chagrin of cellphone carriers, all signs point to text messaging’s continuing its decline in several parts of the world.

In Finland, there was a significant drop on Christmas Eve, one of the busiest days of the year for texting, Tero Kuittinen, a senior analyst at M.G.I. Research, wrote in a blog post for Forbes.

Cellphone customers on Sonera, a Finnish mobile network, sent 8.5 million text messages on Christmas Eve, down from 10.9 million on the same day the previous year, Mr. Kuittinen said, citing a report by the Finnish national broadcasting service. DNA, a Finnish carrier for younger customers, also experienced a decline, with subscribers sending 5.6 million messages, down from 5.9 million in 2010.

In Hong Kong there was a steep decline in text messaging on Christmas Day, down nearly 14 percent compared to the previous year, according to Mr. Kuittinen.

Australians, too, sent fewer text messages — down 9 percent from 2010, according to Richard Blundell, an independent blogger who hashed together data from the Australian Bureau of Statistics and Telstra, an Australian carrier.

The fading allure of text messaging is most likely tied to the rise of alternative services like Facebook, Twitter, BlackBerry Messenger and iMessage, which allow customers to send messages free using a cellphone’s Internet connection, analysts say.

Here in the United States, the number of text messages sent by cellphone customers is still growing, but that growth is gradually slowing, according to John Hodulik, a telecom analyst with UBS. His data, published in June, found that texting in the United States grew 10 percent in the first quarter of 2011. That was down from 16 percent growth in the fourth quarter of 2010.

Mr. Kuttinen said he predicts “SMS erosion” will hit AT&T and Verizon in the next two years.