Other allergies develop under different immunological mechanisms without involving IgE, the most frequent being contact dermatitis due to very small allergens that pass through whole skin and produce a reaction within 24-48 hours at the place of contact. The celiac disease is another allergic disease that does not involve IgE and is due to sensitivity to gluten (a protein in wheat and rye).
However, what is known as an intolerance (for example, to aspirin or lactose) are not true allergies because they do not act as allergens or depend on an immunological reaction to them.