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Your main legal hurdles will involve having someone to manage and oversee the business while you're away. You will need to have a proper street address in the United States where the business will be located--for tax and legal service of process matters. You will have the logistical issue of finding someone to keep current with your mail (or forward it to you), deposit any checks received and pay bills as they come in. You can address many of these issues by signing up with what's known as a "corporate identity package," "virtual office," or "executive suite," which can provide the mailing address, telephone number and mail forwarding services. You will also want to make sure you have an attorney and accountant on your "team" to keep you apprised of any legal issues and tax payments that may arise. As for the day-to-day issues--responding to telephone messages, customer complaints and opening mail--you will need to hire an employee or find a virtual assistant who will handle those tasks.
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