Developments in networking technologies along with the introduction of application-awareness in the network are motivating researchers to turn to the network for providing enterprise solutions. A network-infrastructure grid, consisting of network entities, is one such approach. Such a grid harnesses the idle compute power in the network, and offers transparent network services to end-users. This paper emphasizes the need for autonomy in such grids. Among the autonomous features, certain services have been found to be necessary and some others, desirable. These are discussed using our network-layer grid, namely the iSEGrid. Techniques to customize these features to application requirements are provided. An important contribution made in this paper is a formal framework, based on Abstract State Machines, for specifying, defining an autonomous network layer grid.