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Problems with Microsoft’s (s msft) Hotmail service that surfaced Monday cropped up again throughout the day Tuesday and persisted into the night. Late Tuesday afternoon, a Microsoft spokesman said the company is investigating an issue “affecting a small number of users’ access to Hotmail and Outlook.com” and is working to restore access as fast as possible.

As is usually the case, reports of the outage erupted on Twitter. One user in Austin, Texas said her service had been down for “hours at a time for two days.” She said Hotmail support attributed the issue to system updates. Other Hotmail users reported no problems.

Hotmail, a free basic email service which Microsoft said this summer would be transitioned into a new Outlook.com brand over the next few months, competes with Google’s (s goog) Gmail and Yahoo(s yhoo) mail in the consumer email market. Users on both Hotmail and Outlook.com sites were impacted Tuesday.

Update: See this updated story for more information about Hotmail/Outlook.com problems.

Another update: And, here is another update, on May 2, 2013, Microsoft said the Hotmail-to-Outlook.com migration is complete. Feel free to comment there.