In general, investment in the United States will be in the form of a subsidiary. It is possible for a non-U. S. corporation to operate a branch office in the United States, but there are significant disadvantages to a branch, particularly with respect to its tax treatment.
Branches of non-U. S. corporations are not subject to federal regulation or registration requirements. However, each state will require a "foreign" corporation to "qualify" before "doing business" in that state. A corporation will be considered "foreign" if it is organized under the laws of another country or another state, and so this is not a requirement imposed only on non-U. S. investors.
"Doing business" is a technical term that implies a substantial presence in the state. This would include the ownership or leasing of real property, the maintenance of a stock of goods for local sale, employees and the like. Selling products to local customers, either directly or through an independent sales representative or distributor, would not in itself constitute "doing business".
The states actually exercise little control over the qualification process other than to ensure that the qualifying entity’s name is not confusingly similar to an already registered entity and that all registration fees and taxes are paid (qualification is basically a form of taxation). In most states, qualification for a non-U. S. corporation consists of a relatively easy application, a registration fee, and a notarized or legalized copy of the corporation’s articles of incorporation (in English or a certified translation).