Final answer:
The tissue layers immediately beneath the periosteum are the circumferential lamellae, which are part of the compact bone structure providing support and protection.
Step-by-step explanation:
The layers of bone tissue immediately deep to the periosteum are the circumferential lamellae. The periosteum is a fibrous membrane that covers the bone's outer surface, providing channels for blood vessels and nerves, as well as attachment points for tendons and ligaments.
Underneath the periosteum, the compact bone tissue consists of concentric layers called lamellae, among which the first few layers right under the periosteum are known as circumferential lamellae. These layers run around the entire circumference of the bone, providing structural support and protection.