Thank you for giving me the opportunity to assist you. I will give the best answer that I can with the information provided.
If your girlfriend is not required to file a return and does not file one and claim her own children, then you may claim them as qualifying relatives providing all of the qualifying relative conditions are met, such as residency (live with you all year), you pay more than 1/2 the cost of their support, etc.
Unfortunately, even though you may be able to claim them as dependents, you cannot use them for head of household status, earned income credit, or child tax credit.
Pub. 501 from www.irs.gov has a lot of information regarding dependency if you need more info.
Please let me know if I can assist further.