Can I apply F2A visa for my wife and two minor kids who have British passports and currently visiting me here in the US on ESTA approval visa waiver?

Current visa availability for the F-2A category for the month of February 2014 is up to September 8, 2013. As your wife and children entered under ESTA approvals, they are only allowed to remain for 90 days. Under the present outllok for visa availability, they would not be in legal status at the time that their priority dates clear so that an I-485 adjustment of status application could be submitted. Since you are not a US citizen, they would not be allowed to adjust their statuses if illegal. I suggest your petitioning for them now while they are here, having them return home, and consular processing their cases overseas for green cards.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.