Insufficient gender equality among academic staff in Swedish Higher Education is generally considered as a problem of quality. In an ongoing project different approaches are examined in order to, with departure in available statistics on Higher Education, facilitate wording of one or more hypotheses on why these shortcomings seem to remain. More precise, the purpose of the project is to identify critical phases in crossing from undergraduate studies over to doctoral studies and to an appointment within Higher education with regard to gender and posts for which a doctoral degree is a requirement. In this paper the background of the project is presented and some empirical observations focused on what statistical level (vertical) changes and horizontal statistical changes over time can be observed.. In the middle of the 1990thies Riis & Lindberg (1996) completed a study, including a bibliography, on how male and female applicants qualifications were assessed when they competed for positions at Swedish universities. The point of departure was the then rather common belief that discrimination of female applicants occurred especially in connection with recruitment and that a great amount of research "again and again had shown" that discrimination of females was going on within Swedish Higher Education. The period studied was 1982-1994 and the material was written expert assessments of applicants qualifications and official records from appointments committees. Source material was documentation on 311 staff appointments. The main results were: - Females were found among the applicants in four cases of ten. -A critical test of judgments used, when assessing male and female qualifications, showed that there were no systematically differences in used assessment adjectives. Male and female applicants were treated the same. However in the tested group, females were 22 percent of the applicants but 31 percent of the appointed scholars. Female came out better when they applied for positions in competition with one or more males. This is true for all the studied period. They also found that the situation changed over years in advantage of the females. -Holders of academic positions still were organized in a form of a gendered pyramid. At the top full professors, most of them males. Below that associate professors, most of these males but a growing number females and at the bottom assistant professors and junior lecturers. The third group with a larger number of females. -Studies showing that discrimination was an ongoing activity within the recruitment process could not be found. There were some empirical studies, but these showed that females came out quite well when they competed with males about posts at universities. Their conclusion was that the academic recruitment system not seemed to be the critical point for gender equality within Higher Education. Since then quite a lot have happened. Swedish Higher Education is still expanding. A promotion reform was launched in 1999. The gender equality work still goes on via changes of the Higher education ordinances and through different concrete efforts within the universities. Gender equality has probably improved through "natural filling-up" by females choosing an academic career. Several studies with focus on gender equality within higher education have been conducted during the late 1990thies. As a part of a follow-up of the study above Kyndel, Lindberg and Riis (2003) compiled a Nordic bibliography over the period 1995 - 2002. The purpose was on one hand to construct a picture of where things stand at present, on the other hand to create source material for further studies of gender equality, recruitment and staff appointment within Higher Education. The commented first part of this bibliography consists of about 160 items. The findings from the bibliography are used when critical phases in the available statistics on Swedish Higher Education are identified. Used statistics cover all faculties within Swedish Higher Education.