Multi-licensing is the practice of distributing software under two or more different sets of terms and conditions. This may mean multiple different software licenses or sets of licenses. Prefixes may be used to indicate the number of licenses used, e.g. dual-licensed for software licensed under two different licenses.
When software is multi-licensed, recipients can choose which terms under which they want to use or distribute the software. The distributor may or may not apply a fee to either option. The two usual motivations for multi-licensing are license compatibility and market segregation based business models.
Business models 
Multi-licensing is commonly done to support free software business models in a commercial environment. In this scenario, one option is a proprietary software license, which allows the possibility of creating proprietary applications derived from it, while the other license is a copyleft free software/open-source license, thus requiring any derived work to be released under the same license. The copyright holder of the software then typically provides the free version of the software at little or no cost, and profits by selling proprietary licenses to commercial operations looking to incorporate the software into their own business. This model can be compared to shareware.
Since in most cases, only the copyright holder can change the licensing terms of a software, multi licensing is mostly used by companies that wholly own the software which they are licensing. Confusion may arise when a person outside the company creates additional source code, using the less restrictive license. Because the company with the official code is not the copyright holder of the additional code, they may not legally include this new work in their more restrictively licensed version. Companies may demand outside developers agree to a contributor license agreement, before accepting their work in the official codebase and source code repositories.
Multi licensing is used by the copyright holders of some free software packages advertising their willingness to distribute using both a copyleft free software license and a non-free software license. The latter license typically offers users the software as proprietary software or offers third parties the source code without copyleft provisions. Copyright holders are exercising the monopoly they're provided under copyright in this scenario, but also use multi licensing to discriminate the rights and freedoms different recipients receive.
Such licensing allows the holder to offer customizations and early releases, generate other derivative works or grant rights to third parties to redistribute proprietary versions all while offering everyone a free version of the software. Sharing the package as copyleft free software can benefit the copyright holder by receiving contributions from users and hackers of the free software community. These contributions can be the support of a dedicated user community, word of mouth marketing or modifications that are made available as stipulated by a copyleft license. However, a copyright holder's commitment to elude copyleft provisions and advertise proprietary redistributions risks losing confidence and support from free software users.
Description on one specific example to illustrate multi-licensing: Oracle MySQL comes in various editions: MySQL Enterprise Edition is a commercial edition, hence to be purchased. The license is only offered as a subscription, named MySQL Enterprise Edition Subscription. The same applies for MySQL Standard Edition (MySQL Standard Edition Subscription) and MySQL Cluster CGE (MySQL Cluster Carrier Grade Edition Subscription). The other editions, such as the MySQL Classic Edition or MySQL Community Edition, are free to use (attention to user: some restrictions apply). For instance, the MySQL Community Edition is a freely downloadable version, available under the GPL license and is supported by a community of open source developers.
License compatibility 
A second use of multi-licensing with free software is for license compatibility, allowing code from differently licensed free software projects to be combined, or to provide users the preference to pick a license.
Examples include the source code of Mozilla Application Suite and previously Mozilla Thunderbird and Mozilla Firefox, that have used tri-licensing under the Mozilla Public License (MPL) 1.1, GNU General Public License (GPL) 2.0 or GNU Lesser General Public License (LGPL) 2.1 before the latter upgraded to GPL-compatible MPL 2.0, making the tri-licensing unnecessery; Perl, which is dual-licensed under the GPL or Artistic License; and Ruby, whose license contains explicit GPL dual licensing.
Market segregation in proprietary software 
Multi licensing is also used by distributors of non-free software. Sometimes this is done to proprietary software to segregate a market. By splitting customers into multiple categories such as home users, professional users, and academic users, copyright holders can set different prices for each group. However, among proprietary software companies, it is more common to release a "home edition" and a "professional edition" of a given product, which differ by the software and software features included, not just the license.
See also 
- Business models for open source software
- Commercial use of copyleft works
- Commercial open source applications
- Professional open-source
- Linux News: Tech Buzz: Dual Licensing: Having Your Cake and Eating It Too
- Dual-Licensing Open Source Business Models | Linux
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- Glossary of Software Licensing