Most existing anonymization work has been done on static datasets, which have no update and need only one-time publication. Recent studies consider anonymizing dynamic datasets with external updates: the datasets are updated with record insertions and/or deletions. This paper addresses a new problem: anonymous re-publication of datasets with internal updates, where the attribute values of each record are dynamically updated. This is an important and challenging problem for attribute values of records are updating frequently in practice and existing methods are unable to deal with such a situation. We initiate a formal study of anonymous re-publication of dynamic datasets with internal updates, and show the invalidation of existing methods. We introduce theoretical definition and analysis of dynamic datasets, and present a general privacy disclosure framework that is applicable to all anonymous re-publication problems. We propose a new counterfeited generalization principle alled m-Distinct to effectively anonymize datasets with both external updates and internal updates. We also develop an algorithm to generalize datasets to meet m-Distinct. The experiments conducted on real-world data demonstrate the effectiveness of the proposed solution.