WRAPUP 1-Exxon CEO sees '08 pay rise, Chevron CEO's pay off

* Exxon CEO total pay up 34 pct

* Chevron CEO total pay off 39 pct (Recasts first paragraph, adds details from Chevron SEC filing, background)

HOUSTON, April 13 (Reuters) - Exxon Mobil Corp (XOM.N) Chief Executive Rex Tillerson's total compensation rose 34 percent in 2008 while the head of its largest U.S. rival Chevron Corp (CVX.N) saw his total pay fall 39 percent, according to regulatory documents filed on Monday.

Oil companies experienced a roller-coaster year in 2008. Crude oil peaked over $147 a barrel in July before the global recession hit demand and knocked prices down to about $40 per barrel at year's end.

Tillerson's total compensation was valued at $22.4 million in 2008, up from $16.7 million in 2007. That tally includes salary, bonus, the value of stock awards and change in pension values and deferred compensation.

Tillerson's bonus rose 19 percent to $4 million and his stock awards increased to $7.8 million from $5.7 million.

Exxon's chief was also granted $17.6 million in restricted stock awards in 2008, according to the proxy filing.

The company's board of directors also gave Tillerson an 10 percent salary increase for 2009. His pay will now be $2.06 million.

Total compensation for David O'Reilly, the CEO of Chevron fell to $19.3 million from $31.54 million a year ago. A sharp drop in 2008 stock awards accounted for the bulk of the steep decline, according to the filing.