As states have struggled to balance their budgets by cutting services, laying off workers and raising taxes, a study to be released on Wednesday suggests that many profitable Fortune 500 companies have not been paying as much in state corporate income taxes as the average levied on American companies, with some big firms paying none at all in recent years.

A few companies, including DuPont, reported paying no state corporate income taxes from 2008 to 2010 even as they reported profits, according to the study, which was conducted by Citizens for Tax Justice and the Institute on Taxation and Economic Policy, nonprofit research organizations in Washington that advocate a more progressive tax code. (A spokeswoman for DuPont said that she had not seen the study, but that “DuPont complies with all tax laws and regulations” wherever it operates.)

This year, there has been a great deal of discussion about whether corporations are paying their fair share of federal taxes. But the issue resonates at the state level as well, where corporate taxes have long been a shrinking share of state revenues. While corporate income taxes made up 9.7 percent of state revenues in 1980, according to the Nelson A. Rockefeller Institute of Government, they now make up only an estimated 5.7 percent.

To gauge how much Fortune 500 companies are paying in corporate income taxes, the study looked at the 265 of them that are both profitable and disclose their state tax payments. It found that 68 reported paying no state corporate taxes in at least one year between 2008 and 2010. All together, the study found that the companies reported $1.33 trillion in domestic profits from 2008 to 2010, but paid states only about half of what they would have if they had paid at the average corporate income tax rate of all states — reducing their state taxes by some $42.7 billion.