Go to the Ill DOR website, and check the definition of "capital gains".  Ought to be there.  Next, step down to installment sale.  Finally, look at the items on which non-residents are taxed by IL.  This will provide the rules IL follows......to go into the actual law, then might have to call IL DOR and ask for cites to the actual law.

You owe IL tax, because you sold property located in IL........and have an ongoing interest in that property, until  end of contract or foreclosure/cash sale, whichever comes first.

Typically, any tax you pay to another state as a non resident of that state can then be taken as a credit on your residential state........since the residential state will also tax you on that income.

For example............if an Iowa resident, Iowa computes the AMOUNT of the tax related to the non-resident item in effect as if the item were at the top of the person's income stream, when applying a bracket.........and then allows a credit against any tax paid to another state at the lesser of the non-resident state's tax, or the amount of Iowa tax paid on that item.

Iowa's brackets are so high that seldom does the credit amount to any more than the actual state tax paid to the non-resident state.

Also....... be alert that the capital gains might NOT be taxed at all by one or both states, totally depending upon the circumstances of the sale.

In Iowa, for example, if a farmer sold his land, and depending upon how long he had farmed it etc etc.........the capital gains portion might not be taxed by the state, even on installment sales.