Establishing a business in the United States as a non-U.S. citizen involves several key rules and regulations. Here are some important points to consider:

1. Legal Structure: Non-U.S. citizens can set up various types of business entities, such as Limited Liability Companies (LLCs), Corporations (C Corps or S Corps), or Partnerships. The choice of legal structure affects taxation, liability, and regulatory requirements.

2. Visa Requirements: Depending on the business activity, a non-U.S. citizen may need a suitable visa to operate a business in the U.S. Common visa categories include:

   • L-1 Visa: For intra-company transferees.
   • E-2 Visa: For investors in a business.
   • H-1B Visa: For specialty occupations.

3. Registered Agent: A business must have a registered agent with a physical address in the state where the business is formed. This agent receives legal documents on behalf of the business.

4. Business License and Permits: Depending on the location and type of business, specific licenses and permits may be required. This can include state, local, and federal licenses.

5. Employer Identification Number (EIN): An EIN is necessary for tax purposes, especially if the business has employees. Non-U.S. citizens can apply for an EIN through the IRS.

6. Opening a Bank Account: Non-U.S. citizens can open a business bank account in the U.S., though they may need to provide documentation such as an EIN, business registration documents, and identification.

7. Compliance with Local Laws: Businesses must comply with local, state, and federal regulations, which may vary significantly depending on the industry and location.

8. Taxation: Non-U.S. citizens may be subject to different tax rules. It’s essential to understand both federal and state tax obligations, and it may be advisable to consult with a tax professional.

9. Foreign Ownership Limitations: Certain industries, such as telecommunications and aviation, may have restrictions on foreign ownership. It's crucial to check industry-specific regulations.

If you're considering establishing a business in the U.S., consulting with legal and business professionals is highly advisable to ensure compliance with all relevant laws and regulations.