If you are allergic to nuts there are good substitutes such as olives, pumpkin seeds, sunflower seeds and avocados and are all excellent sources of the nutrients, including unsaturated fats, that nuts are famous for. Nuts are usually high in many nutrients, fat and protein. Anything with an edible kernel and hard shell is defined as a nut. This includes true nuts like chestnuts and acorns, but also things such as seeds, like Brazil nuts, or legumes, like peanuts.