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U.S. source capital gain, which is not effectively connected with a US trade or business ("effectively connected" is a special tax term generally meaning that it the assets are used in an active US trade or business - sale of stock in an individual portfolio is not "effectively connected" with a US trade or business), that is realized by a nonresident alien from the sale or exchange of a capital asset is not subject to U.S. tax. unless it is:

(1) capital gain from what would ordinarily be a capital asset which is considered under the Internal Revenue Code as gain from an asset that is not a capital asset, if such gain is treated as "fixed or determinable income" under the Internal Revenue Code;
(2) gain from the sale or exchange of a U.S. real property interest; or
(3) gain realized by a nonresident alien during a taxable year in which he is present in this country for an aggregate of 183 days or more.

All of this can be found in Section 871 of the Internal Revenue Code and the associated Regs. The "effectively connected" stuff is in Section 864 and the Regs for 864.
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