Web directory and search engines are different animals. Search engines are databases. If your site is indexed by a search engine, it means your site is stored in their database. If your site is indexed by a web directory, it means your site appear on some page of the directory. For example, if your site is indexed by ur lsubmission net directory, under category Family->Pets, your site will appear on the page Pets. The most famous web directories are DMOZ and Yahoo directory.

A list of web directories you can submit your urls.

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