My ex-husband and I purchased an old house from his Grandmother in 1994. In 1997 he quit claimed his part of the house to me in a divorce settlement. Since then I have learned that the Grandmother's inherited the house from her father and that the step-mother of the Grandmother seems to have some claim in the house. All of these people are deceased except for my ex. How do I get a marketable title?

You will have to file a lawsuit to quiet title. When you and your ex bought the house from his grandmother did you happen to buy a title insurance policy? If so, call the title company and let them get started.

If you don't already have a title policy then the first step is to call a title agency and order a title search. The results of the search will give you an idea of the next step you need to take. The title agency may be able to clear the issues or you may need to get an attorney.

My ex-husband and I purchased an old house from his Grandmother in 1994. In 1997 he quit claimed his part of the house to me in a divorce settlement. Since then I have learned that the Grandmother's inherited the house from her father and that the step-mother of the Grandmother seems to have some claim in the house. All of these people are deceased except for my ex. How do I get a marketable title?
What gives you cause to suspect that you don't have marketable title? There are all kinds of dormant title claims, some going back hundreds of years. Most of them are not taken seriously and don't affect marketability of title.

Did you have title insurance when you bought the property in '94? Ask the title insurance company to straighten it out.