An electronic web document as an object for recording scientific and cultural communications is considered in the paradigm of library documentology. The research significance of preserving network documents as having a specific temporality of media objects is substantiated. Ego-documents, which include online documents (blogs and forums), are considered as part of media culture that is subject to archiving and has research potential. The problem of the disappearance of web documents and ways to solve it are considered. Archiving web documents as a practice for preserving cultural heritage is justified from the point of view of media archeology. An overview of the activities of domestic and foreign libraries in the formation and development of web archives is presented. Cases of cooperation between national and municipal libraries in the formation of web archives and providing access to electronic documents are presented. Recommendations for the development of web archiving in Russia are proposed.