Can I claim my step kids on my taxes since theyer not blood kin and since they lived with me

Please confirm: you and the kids' mom are married, and you all living together in the same household, right? If so you should probably file as Married Filing Jointly (as opposed to Married Filing Seperately), and include both children as dependents.

I agree with ebaines.

However, to answer your question, if you are married to their mother, the children are legally considered to be your step-children, and you can legally claim them as dependents, provided you meet the other criteria.