The Second-party developer reference article from the English Wikipedia on 24-Apr-2004
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Second-party developer

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In the video games industry, a second-party developer is a developer who, while being a separate entity from any console manufacturer, is tied to a specific one to the exclusion of others. Examples:

Compare to first-party developer, third-party developer.

(To be honest, the line between first- and second-party developers is a blurry one - the defining characteristic is that second-party developers stand out from the manufacturer, while first-party developers are considered to be more or less a "division" of the console maker itself.)