This paper analyzes the determinants of women’s representation on boards of directors based on a panel of all privately owned or listed Danish firms with at least 50 employees observed during the period 1998–2010. We focus on the directors who are not elected by the employees and test three hypotheses on female board representation that we denote the female-led hypothesis, the tokenism hypothesis, and the pipeline hypothesis, respectively. We find evidence rejecting the female-led hypothesis. Firms with a female chairperson on (...) the board of directors tend to have significantly fewer other non-employee-elected female board members. We also find clear evidence of a tokenism behavior in Danish companies. The likelihood of enlarging the share of non-employee-elected female board members is significantly smaller if one, two, or more women have sat on the board of directors. Finally, the pipeline hypothesis is partly confirmed. The relation between the female pipeline of potentially qualified directors and female directors is weaker than the similar relation for males. Our findings offer insights to policy makers interested in promoting gender diversity within boardrooms. Our empirical evidence suggests that an important way to increase the female proportion of non-employee-elected board members is that more women reach top executive positions. (shrink)