Mobility management is a desired feature for the emerging Internet of Things (IoT). Mobility aware solutions increase the connectivity and enhance adaptability to changes of the location and infrastructure. IoT is enabling a new generation of dynamic ecosystems in environments such as smart cities and hospitals. Dynamic ecosystems require ubiquitous access to Internet, seamless handover, flexible roaming policies, and an interoperable mobility protocol with existing Internet infrastructure. These features are challenges for IoT devices, which are usually constrained devices with low memory, processing, communication and energy capabilities. This work presents an analysis of the requirements and desirable features for the mobility support in the IoT, and proposes an efficient solution for constrained environments based on Mobile IPv6 and IPSec. Compatibility with IPv6-existing protocols has been considered a major requirement in order to offer scalable and inter-domain solutions that were not limited to specific application domains in order to enable a new generation of application and services over Internet-enabled dynamic ecosystems, and security support based on IPSec has been also considered, since dynamic ecosystems present several challenges in terms of security and privacy. This work has, on the one hand, analysed suitability of Mobile IPv6 and IPSec for constrained devices, and on the other hand, analysed, designed, developed and evaluated a lightweight version of Mobile IPv6 and IPSec. The proposed solution of lightweight Mobile IPv6 with IPSec is aware of the requirements of the IoT and presents the best solution for dynamic ecosystems in terms of efficiency and security adapted to IoT-devices capabilities. This presents concerns in terms of higher overhead and memory requirements. But, it is proofed and concluded that even when higher memory is required and major overhead is presented, the integration of Mobile IPv6 and IPSec for constrained devices is feasible.