Slugs, like all mollusks, do not have brains in the traditional sense. Instead, slugs' nerve cells are concentrated in tight knots, called ganglia, in important parts of the body.
Mollusk nerve cells lack a myelin sheath, which is a fatty shell found around the nerve cells in vertebrate creatures that is used for the conduction of electrical signals between nerve cells. Giant axons have developed in more highly developed mollusks, such as the cephalopods, which include squid and octopi. The large size of these nerve cells allows the faster transport of electrical signals without the aid of a myelin sheath.