We generalize the Bondi-Sachs treatment of the initial-value problem using null coordinate systems. This treatment is applicable in both finite and asymptotic regions of space whose sources are bounded by a finite world tube. Using the conformal techniques developed by Penrose, we rederive the results of Bondi and co-workers and of Sachs in conformal-space language. Definitions of asymptotic symmetry "linkages" are developed which offer an invariant way of labeling the properties of finite regions of space, e.g., energy and momentum. These linkages form a representation of the Bondi-Metzner-Sachs asymptotic symmetry group.