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Eee PC shipments will rise to between 1.2 million to 1.3 million units in the three months ending 30 June, said Asustek, with the company shipping 700,000 Eee PCs in the first quarter.

Shipments of the Eee PC have gone up so fast that they are starting to challenge the company's other laptop PC products.  Overall Asustek says it will sell between 1.3 million and 1.4 million notebook PCs during the second quarter, up from 1.3 million in the first quarter.

However the report also notes that the device will likely face a lot more competition in the future. Several other companies, including Acer, MSI and Giga-byte Technology have all revealed plans to market a low-cost laptop similar to the Eee PC.