You will not believe it, but yes. A headless cockroach can survive for several weeks. First of all, this is due to the fact that the head is not such an important organ for them. The absence of a venous and arterial system, the body’s ability to breathe without a head, and a lesser need for food are the main factors that give cockroaches such a unique and unusual ability. If you want to know more, I highly recommend you to read this article about the Cockroaches Myths.