SAN FRANCISCO, Aug. 27 — Acer, the Taiwan-based maker of personal computers, said Monday that it had reached an agreement to acquire Gateway for $710 million, a move that reorders the competitive landscape both here and abroad.

The deal gives Acer a well-known brand name in the United States market and better access to crucial retailers, like Best Buy and Circuit City, computer industry analysts said. The deal may also help Acer build its market share in Europe.

Through a previous agreement, Gateway has the first right of refusal to buy Packard Bell, a computer maker with a relatively strong presence in Western Europe. Acer indicated on Monday that Gateway intended to go forward with an acquisition of Packard Bell.

“Acer is making a double play here,” said J. P. Gownder, an analyst with Forrester Research.

Acer said it planned to pay $1.90 a share, a 57 percent premium over Gateway’s Friday close. The agreement brings to an end the independence of Gateway, which has experienced an erosion of its fortunes and prominence in the last decade.

The deal underscores the increasingly global nature of the personal computer market. Acer, which has its headquarters and chief executive in Taipei, has a president based in Italy. It is in a fierce competition with Lenovo, based in China, to become the world’s third-largest computer maker behind Dell and Hewlett-Packard.

Lenovo, which in 2005 acquired the personal computer business of I.B.M., has indicated it would be interested in acquiring Packard Bell to bolster its own European position. But that prospect appears to be blocked by Acer’s deal to acquire Gateway.

There are challenges for Acer — particularly in marketing multiple brand identities in the American market, industry analysts said. Acer has marketed itself as a relatively high-end brand, while Gateway has catered to the lower end of the market with its brand, emachines.

“The question is how they’re going to manage the brands and channels,” said David Daoud, an analyst with IDC Research. He added that another risk was that Acer was “acquiring a company that is losing market share.”

IDC reported that in the second quarter, Gateway had 5.6 percent of the personal computing market in the United States, while Acer had 5.2 percent. Combined their market share puts them third behind Dell, with 28.3 percent, and Hewlett-Packard, with 23.4 percent.

Richard Black, a spokesman for Acer America, said the company hoped to capitalize on greater access to American retailers; Acer began selling at Best Buy only this year and in Circuit City in 2006, he said.

In Europe, IDC said, Acer had 14 percent market share in the second quarter; if it adds Packard Bell’s 3 percent market share, it could leapfrog Dell and become the second-largest vendor there, behind Hewlett-Packard.

Size matters in the PC industry, as shown by the success of the computer business of Hewlett-Packard, which was combined with that of Compaq.

Acer said that it expected the deal to give it size and scale to allow it to cut procurement and component costs.

Mr. Daoud said the broader challenge for Acer and its competitors is that the demand for desktop computers has been sluggish in recent years and the products have increasingly become commodities.

Hewlett-Packard, Dell and to some extent Acer have sought to diminish the impact of the commodity trend by marketing computers as highly personal and stylish devices rather than one-size-fits-all products. The companies that have grown the fastest in the last year, including Hewlett and Acer, have had strong sales of notebook computers.

The Gateway acquisition will have little effect in the Asian market, outside of Japan, where Lenovo leads with about 21 percent of the market. Acer has 6.6 percent, according to IDC.

The deal is a relatively quiet exit for Gateway, which once was synonymous in the United States with direct-to-consumer sales. Stung by the slowdown of computer consumption and falling prices and margins, the company’s share price has fallen far from the heights of November 1999, when it hit $82.50. It closed at $1.82 Monday.

Mr. Black said that Acer had not decided what it would do with Gateway’s existing brands and whether it might include them in the Acer brand.