The paper analyses Grid networking resource virtualization technologies and requirements in the context of computational mobility. The mechanisms of network virtualization supported by Xen and xVM/Crossbow are presented and compared. A network virtualization model, consisting of three layers, is presented. Changes in virtual network infrastructures resulting from VM or zone mobility are investigated in detail. Typical migration process scenarios are presented, in addition to system commands used prior to and following migration in order to restore network communication. The concept of automating this process is also described.