This dataset contains the digitised censuses which were created in the NWO-funded Replication Study '(Re)counting the Uncounted. Replication and Contextualisation of Dutch and Belgian Premodern Population Estimates (1350-1800)'. In total, close to 2,000 premodern censuses (of hearths, houses, communicants, individuals, etc.) in the Low Countries were identified and catalogued. Around 750 of these were used by one or more of the four studies that were replicated in the study. The first batch of completed censuses can be found in this dataset. More data will be added incrementally. All files are plain text files that contain tab-separated-values (TSV). The file names of the censuses refer to the census identifier which is defined in our catalogue. That catalogue also contains definitions of the units that are being counted (up to 15). For contextual information on the census, we refer to the typology, which is under development and will be made available here in due course. Links between the census observations and GIS polygons of pseudo-territories in the Historical Atlas of the Low Countries, 1350-1800 will be available here.A codebook for the census files, definitions of the bibliographical references and the two-letter territorial codes, and an empty data entry form, we refer to the project's documentation. Note that some of the censuses have space to include fifteen unit variables, whereas older ones have only ten. Other than this, the older censuses are fully compatible with the newer census files. Searching for specific census files works best by using an asterisk: *HO for all censuses pertaining to Holland, or *1469 for all censuses associated with the year 1469. However, be aware that the census identifiers (a two-letter territorial code and the year) carry no meaning of their own. Observations within a census can be linked to more than one year and to localities that are located in different sovereign territories. Last but not least, especially when you use specific digitised censuses from this dataset, it is considerate and generally good practice to also cite the original works that published the census data. Hundreds of authors have worked hard to unlock and sometimes analyse these censuses and it is important to continuously give credit to their efforts.