This paper discusses the cancellation of linear intersymbol interference (ISI) in two-dimensional (2-D) systems. It develops a theory for the error rate of receivers that use tentative decisions to cancel ISI. It also formulates precise conditions under which such ISI cancellation can be applied effectively. For many 2-D systems, these conditions are easily met, and therefore the application of ISI cancellation is of significant interest. The theory and the conditions are validated by simulation results for a 2-D channel model. Furthermore, results for an experimental 2-D optical storage system show that, for a single-layer disk with a capacity of 50 GB, a substantial performance improvement may be obtained by applying ISI cancellation.