My daughter and granddaughter lived with me throughout the year while her husband was living away on active duty. Can I claim them as other dependents if they filed also?

[Opus 17]

You must coordinate with them.  It's possible but not likely.

1. First, your daughter only qualifies as your dependent if she had less than $4300 of taxable income, unless she was under age 24 and also a full-time student.  

2.  You also can't claim your daughter as a dependent if she filed a joint return with her spouse.

3. You could claim your granddaughter as a dependent if you meet all the following tests,

1. she lived in your home more than half the nights of the year
2. she was not claimed as a dependent by anyone else (including her father or mother)
3. you have more taxable income on your return than the mother (if she filed separately) or you must have more taxable income than both parents together (if they filed jointly).

Most of the time, the largest tax benefit would be for the parents to file jointly and claim their own daughter as a dependent, even if the father was out of the country.  No matter any other test, the mother gets absolute first right to claim her daughter as a dependent.  So you would have to have a discussion and coordinate your tax return with your daughter and son-in-laws tax returns to make sure all the rules were followed, assuming they were in agreement with you doing this. 

[Hal_Al]

Q.  Can I claim them as other dependents if they filed also?

A. No. A person can only be claimed on one tax return.

As Opus17 explains, it's possible for you to claim them, depending on the details,  and requiring them to adjust their filing(s).  It is highly unlikely that would work out best for the family.  Doing practice returns and comparing the results, before actually filing, is highly recommended.  The grandchild would most likely qualify as a "qualifying child" rather than an "other" dependent.