Sponges do not have nervous systems, but a glass sponge has a unique set-up that allows it to conduct electrical impulses around its body in response to stimuli from outside. As its body cells divide, they do not separate completely. They remain connected by bridges of cell material, resulting in a mega-cell that looks like a spider web. This web of soft tissue (called a syncytial network) is wrapped around a mineral skeleton for support. When the mega-cell gets stimulated by something outside, an impulse travels rapidly from one part of the sponge to another, across the cell-cell bridges. This function is similar to what our nervous system does, and may allow a glass sponge to respond to signals from its environment.
Glass Sponge
Euplectella