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In order to claim the children-
Normally the child has to live with you for atleast half of the year. If you are a non custodial parent(meaning child did not live with you for greater part of the year)
A child will be treated as your qualifying child if all of the following apply.
Are divorced or legally separated under a decree of divorce or separate maintenance,
Are separated under a written separation agreement, or
Lived apart at all times during the last 6 months of the year.
The child received over half of his or her support for the year from the parents.
The child is in the custody of one or both parents for more than half of the year.
Either of the following applies.
The custodial parent signs a written declaration, discussed later, that he or she will not claim the child as a dependent for the year, and the noncustodial parent attaches this written declaration to his or her return.
A pre-1985 decree of divorce or separate maintenance or written separation agreement that applies to 2007 states that the noncustodial parent can claim the child as a dependent, the decree or agreement was not changed after 1984 to say the noncustodial parent cannot claim the child as a dependent, and the noncustodial parent provides at least $600 for the child's support during 2007
So in short, if you ex wife does not sign a declaration waiving her right to claim the children than you cannot claim them as dependent.
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.