This paper analyzes the determinants of women on the boards of directors based on a panel sample of all Danish companies in the private sector with more than 50 employees. The share of women on the boards of directors was 12 percent in 2007 and has only slowly increased during the period 1997-2007. We test three hypotheses on female board representation which we denote the female-led hypothesis, the tokenism hypothesis, and the pipeline hypothesis, respectively. Based on fixed effects estimation we find that the female-led hypothesis cannot be supported. Firms with a female chairman of the board of directors tend to have significantly fewer other non-staff board members. We find clear evidence of a tokenism behavior in Danish companies. Having one non-staff woman on the board is negatively related to the chance of hiring another woman for the board of directors. Finally, the pipeline hypothesis is partly confirmed. The share of women among the group of CEOs and VPs from other firms in the industry is positively related to having a women on the board.