can an illegal woman apply for citizenship if her children are american citizens

Unfortunately no. Your children would have to be the age of 21 before they could begin to sponsor you for green card. Assuming that they are able to do so, you would have to wait another 5 years to file for U. S. citizenship. If you entered the country legally, and had no other bars than of being an overstayed alien, you would be eligible to adjust status to permanent residence in the U. S. without having to leave the country. However, if you entered the country Illegally and do not have the benefit of section 245(i) (which allows adjustment of status upon payment of a fine to those who entered the U. S. illegally, had a labor certification application or immigrant visa petition filed on their behalf by April 30, 2001 and were physically present on December 21, 2000), you would not be eligible to adjust status and if you left the U. S. to consular process your immigrant visa case based upon your children’s petition, you would be barred from returning to the country for 10 years unless you obtained a waiver based upon extreme hardship to a U. S. citizen or permanent resident spouse or parent. Another option is to wait and see what happens with the comprehensive immigration reform legislation which is currently the focus of attention in the House of Representatives. Such may eventually lead to a pathway for citizenship. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.