zero income

What type of company?

If you have a corporation (C or S), you have to file an income tax return (1120 or 1120-S) regardless of whether or not your corporation has any income.

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@Gevkeep wrote:

...I have a company with zero income.what should i do?

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Also note, if you have something like a sole proprietorship, you might still have expenses which would result in a net loss for the business (which could be useful in terms of offsetting other income).