Machine-to-Machine communications (M2M) allow connected devices to exchange data and perform actions without human intervention. Different M2M applications have different quality of service (QoS) requirements. The dynamic QoS control is critical for applications like video surveillance, transportation services, and industrial control. The provided QoS depends on device connectivity. Connectivity management provides centralized management of M2M devices and connections. The paper studies model aspects of QoS management for connected M2M devices by means of connectivity management. Models for connectivity management are suggested, formally described and verified. The capabilities for device connectivity management are used to model the behavior of autonomous agent for dynamic QoS control.