"Program Fragments, Linking, and Modularization" Luca Cardelli Report #144, February 15, 1997. 25 pages. Module mechanisms have received considerable theoretical attention, but the associated concepts of separate compilation and linking have not been emphasized. Anomalous module systems have emerged in functional and object-oriented programming where software components are not separately typecheckable and compilable. In this paper we provide a context where linking can be studied, and separate compilability can be formally stated and checked. We propose a framework where each module is separately compiled to a self-contained entity called a linkset; we show that separately compiled, compatible modules can be safely linked together.