My boyfriend passed away a year ago and his estranged wife had left him a year before he passed abandoning there two children. After his passing I still kept in contact with the children. Currently his ex is living in a car and the children have been living with me for two months, is there anyway of establishing guardianship even though I am not a family member?

Does the mom agree? If so, go to a lawyer and have papers drafted and filed with the courts. If not, then you may have to get CPS involved and have them place the children with you if they can't find a blood relative to take them. You will need a lawyer for the paperwork either way; you want to make sure its done correctly.