This study takes up the point that it requires a certain kind of educational institution to deliver a certain kind of education to ask why do we have private higher education in Australia, what is the non self-accrediting institution (NSAI) and what type of so-called ‘non-university’ higher education are they providing students? The purpose of this study is to explore why Australia has the ‘private’ higher education sector it does and to provide an account for its existence and growing presence from 1980 to 2010/2018. This study is timely given increased policy directions for an ‘inclusive and seamless tertiary education sector’, the anticipated rise in enrolments in ‘private’ higher education and discussion and debate on the costs associated with providing higher education in a neoliberal state. The study is undertaken as a qualitative case study, and includes a detailed exploration of related policy during the period of the study. Based on a critique of the uses of Levy's typological system to describe Australia's non-university sector, a new localised and contemporary typology for Australia's NSAIs was developed to contribute to the explication and explanation for the growth in numbers of NSAIs.