A distant relative died. He had NO will, no spouse and no children. The state has included as an heir my deceased nephew's illegitimate daughter. My nephew never married the mother of this girl. Also included as heirs are my deceased brother's two sons. My sister and I who are in our 60's are first in succession. Why are all of these young people included? I would think they would inherit later if at all.

Rules of inheritance are determined by state law; in other words, the 'state' tells the deceased where his property is going, not that the state takes it, as some folks say.
I believe your question involves distribution per capita and distribution per stirpes. Check this: Per stirpes - Wikipedia, the free encyclopedia
The chart may be beneficial to you.

As George said, state laws govern intestate inheritance. And since you left out that vital piece of info, we can't advise specifically. Generally such inheritance is tiered. So if there are relatives in one tier it stops at that tier. But generally all the relatives in fit into a tier inherit equally. To advise further would also require the actual relationships to the deceased.