The independence theorem of Kim and Pillay is one of the main results about forking in simple theories. It turns out that a weak form of the independence theorem can be formulated and proved in a much larger class of NTP2 theories (introduced by Shelah and containing both simple and NIP theories). As an application, we show that over extension bases for non-forking in NTP2 theories, Lascar strong type is equivalent to Kim-Pillay strong type. Joint work with Itai Ben Yaacov.