Much like the refunds in the summer of 2001, which were also a product of a Bush tax cut, checks will go first to those who filed returns by April 15. Those who asked for filing extensions may also get refunds, but theirs won't be mailed until four to six weeks after their returns are processed.

Here's a look at who will get refunds, when they will get them and how the refunds may affect returns for the 2003 tax year.

Q. What are the checks for?

A. The new law boosts the child tax credit from $600 to $1,000 per eligible child for the 2003 and 2004 tax years. The refund checks are an advance on the higher credit that parents are now expected to claim for 2003. (The IRS won't send checks for the entire credit amount because most families account for their credits and deductions in their payroll withholding. Sending a check for the entire credit could result in underwithholding.)

Because the IRS can't be sure who will claim the child tax credit in 2003, it's sending checks to taxpayers who claimed the credit for the 2002 tax year.

Q. How much will I get?

A. That depends on two factors: How many children you have and how much tax you paid on your 2002 income.

Most middle-income parents — those with adjusted gross income of between about $40,000 and about $110,000 — will receive the full amount of $400 per eligible child. However, some lower-income parents will receive less. Some high-income parents will receive nothing.

Q. Why will lower-income parents get less or nothing?

A. The child tax credit can't reduce your federal income tax below zero. Many low-income families pay less than $400 in tax per eligible child, so their tax refund generally would amount to the lesser of the credit amount or the amount of tax they paid.

There's one exception: Low-income families who qualify for another tax break known as the "additional child tax credit" may get somewhat more than the federal income tax that they paid. But the calculation to determine exactly how much they'll get is complex. The IRS will calculate the amount for taxpayers, based on the information provided on 2002 returns.

The New York Times Web site reported last night that most families with incomes from $10,500 to $26,625 will not benefit.

Q. Why might high-income families not get anything?

A. The child tax credit is limited by income. Singles with adjusted gross income of more than $75,000 and married couples with more than $110,000 lose $50 of the credit for each $1,000 that their income exceeds the threshold.

Q. Will anyone else who claimed the credit on a 2002 return not get a check?

A. Yes. The IRS will also exclude taxpayers whose children were born before 1986, since the credit only goes to those with children who will be under 17 at the end of 2003.

Q. When can I expect a refund?

A. Refunds are going out based on the last two digits of the first Social Security number listed on each return. Checks to those with Social Security numbers ending between 00 and 33 will be mailed on July 25; checks to those with numbers ending in 34 to 66 will be mailed Aug. 1; those with higher numbers can expect checks after Aug. 8.

Q. What if I get a check for more than I'm due?