Removing Grease on Kitchen Cabinets?

My kitchen doors are wooden chestnut, but are hard to clean. They keep on getting splashed near the cooker and the slightest grease mark shows up really badly. Over the years I have cleaned them with certain cleaners, but when the sun shines you can still see the marks. Is there a cleaner that is quick and safe to use on wooden unit doors. Help.

By R Farrow