Only on the children's own tax returns if they are required to file one. You cannot put your child's income on your tax return.
2016 Filing requirements for dependents.
Federal Dependent filing requirements: (State requirements may be different)
1) Dependents unearned income was more than $1,050.
2) Dependents earned income was more than $6,300.
3) Dependents gross income was more than the larger of-
a) $1,050, or
b) Dependents earned income (up to $5,950) plus $350.
Or Dependent had net earnings from self-employment of at least $400.
However, if any tax was withheld, then Dependent might want to file anyway to get a refund of the tax withheld.
Also, a person that CAN be a dependent cannot claim him/her self and must check the box that says that another taxpayer can claim them (whether or not that taxpayer actually claims him/her).
Note: your state filing requirements might be different than the federal.