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Maybe it was not called "Responsive layout", but it was a thing since 2004: https://www.themaninblue.com/writing/perspective/2004/09/21/

Flash was as bad as Java Applets. They both tried to solve problems that couldn't be done with standard web technologies at the time. They both needed extra plugins so they could work... while everything else just works in the browsers. They have no place in web development.

If by "responsive layout" one means adapting to the size of the browser window, and not specifically adapting to mobile screens, then it was fairly common in 2009. And even earlier - we just did it with tables in late 90s and early 00s.

It is also true that the vast majority of web pages done in Flash did not do it.

Maybe not responsive, but definitely fluid design.