My mother is a resident alien living with us for most of the year. Is she required to file an income tax return? Her only source of income is a small annuity from my father's retired military pension (non-US).

If she is a resident alien, ALL world-wide income is subject to U.S. income taxes.

If the pension is less than $3,600, she owes ZERO tax and has NO requirement to file.

Further, she is entitled to a $3,600 personal exemption and a $5,500 standard deduction, so if the total pension is LESS than $9,100 for the year, she will owe ZERO federal income tax, though she WILL have to file a tax return.

First, if your mother is 65 or older she will receive a somewhat higher standard deduction than the $5,500 mentioned above.

Second, the military pension falls under the "Government Service" article of all US tax treaties. What country is your mother from?