* Saudi banks underperform
* Much activity focuses on second-, third-tier stocks
* Travel agency Al Tayyar surges
* Two Oman telecommunications firms tumble
* Other Gulf markets closed for New Year
By Andrew Torchia
DUBAI, Jan 1 (Reuters) - Saudi Arabia's stock market rose on Sunday with much activity focusing on second- and third-tier stocks rather than blue chips, while Oman's bourse was dragged down by a higher tax on telecommunications companies.
The main Saudi index added 0.4 percent. Banking stocks were soft but major gains were seen in a few stocks such as conglomerate Jazan Development, which jumped 5.4 percent after announcing a 0.50 riyal per share dividend for 2016.
Saudi Automotive Services surged its 10 percent daily limit after saying it would post a special gain of 4.4 million riyals ($1.2 million) for the fourth quarter after selling two of its equities investment portfolios.
Travel agency Al Tayyar, beaten down last year by the slump in Saudi consumer spending, climbed 7.4 percent in unusually heavy trade.
Nama Chemicals plunged its 10 percent daily limit for a second straight day. It resumed trading last week after its shares were suspended for a day because its accumulated losses had reached more than 75 percent of its capital. The company now plans a capital reduction.
In Oman, the stock index dropped 0.7 percent as Oman Telecommunications tumbled 4.3 percent and rival Ooredoo Oman sank 7.9 percent.
On Thursday, the Capital Market Authority said Oman's telecommunications companies would pay a royalty to the government of 12 percent of revenues in 2017, up from 7 percent.
Other markets in the Gulf, as well as Cairo's exchange, were closed for New Year holidays.
* The index added 0.4 percent to 7,238 points.
* The index fell 0.7 percent to 5,745 points.
Editing by Adrian Croft