Paper that has been soaked in oil to make the paper water resistant and translucent. The paper is heavier due to the weight of the oil and also smells like oil.
The pictured booklet dates from 1938 and is still translucent, though it has dried out quite a bit over time. It was stored several years in plastic sleeves and the oil has permeated the plastic. Care should be taken to separate material in oilpaper from other items.