Among children in the United States, around one percent is allergic to peanuts; nine percent have asthma. Among asthmatic kids, 75 to 80 percent have some type of allergy. There doesn't seem to be a direct cause-effect relationship between allergies and asthma, but among those children who suffer from both peanut allergies and asthma, it appears that an allergic reaction to peanuts can set off an asthma attack. Since one of the symptoms of an allergic reaction to peanuts is swelling and inflammation, the allergic reaction can end up inflaming bronchial tubes and inducing an asthma attack. Plus, allergies appear to worsen the severity of asthma attacks.
Still, it isn't common for peanut allergies to trigger asthma, and most researchers are hesitant to draw any direct correlation between the two. If a child has both asthma and peanut allergies, though, he's still better off being extra careful to avoid an allergic reaction.