The second-largest oilfield services company, Halliburton (NYSE: HAL), followed industry leader Schlumberger (NYSE: SLB) Monday in reporting reasonably solid quarterly results. And even more importantly, the company's management echoed Schlumberger's earlier predictions that even better times are ahead for the sector.

For the quarter, Halliburton checked in with earnings of $584 million, or $0.64 a share, versus $552 million, or $0.54 per share, in the first quarter of 2007. Revenues were up 18% year over year. The most recent quarter experienced a special items "wash" from a $0.02 after-tax impairment charge relating to oil and gas property in Bangladesh, exactly offset by a two-penny gain from the sale of a joint venture interest. Revenue outside the U.S. grew 24%, while non-U.S. operating income was up by 21%. Domestic revenue growth was 11% for the quarter.

Dave Lesar, Halliburton's CEO, who slightly more than a year ago announced the opening of a headquarters in Dubai to better service the Eastern Hemisphere, said, "Our first quarter results were consistent with our previously announced expectations. Our international revenue growth helped offset the production enhancement pricing pressures we knew were coming in the U.S. market."

Halliburton's Completion and Production (C&P) segment and its Drilling and Evaluation (D&E) unit increased their operating income by 11% and 6%, respectively. And from the more important perspective of future directions, Lesar said that, "The fundamentals of the world oil and gas market are projecting that the next leg up in this extended cycle is near."

As to areas of geographic strength and weakness, in addition to U.S. softness, the company noted that its quarter was affected by general weakness in the North Sea and Nigeria, and by reduced fracturing activity in Russia. But while the first two areas are likely to remain slow, Russia appears set to recover.

So with the two biggest service companies having reported sound, if unspectacular, earnings increases for the quarter -- along with Weatherford (NYSE: WFT) -- we'll now await word from other members of the sector. I'll be especially interested in results from the two big deepwater drillers Transocean and Diamond Offshore.

As to Halliburton, I believe that the company is benefiting from Lesar's new digs in Dubai and from a number of other moves he's made at Halliburton, including the jettisoning of KBR (NYSE: KBR), its former engineering and construction subsidiary. Beyond all that, I concur with his assessment that the fundamentals of world oil and gas bode well for the industry, clearly including his company.

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Fool contributor David Lee Smith wishes he could own shares of Halliburton, but he can't for now because of his fetish for writing about the company. He does welcome your questions or comments. The Fool has a disclosure policy.