The results of a comprehensive statistical analysis of gender systematics in the time allocation process at ESO are presented. The sample on which the study is based includes more than 13 000 Normal and Short proposals, submitted by about 3000 principal investigators (PI) over eight years. The genders of PIs, and of the panel members of the Observing Programmes Committee (OPC), were used, together with their career level, to analyse the grade distributions and the proposal success rates. Proposals submitted by female PIs show a significantly lower probability of being allocated time. The proposal success rates (defined as number of top ranked runs over requested runs) are 16.0 ± 0.6% and 22.0 ± 0.4% for females and males, respectively. To a significant extent the disparity is related to different input distributions in terms of career level. The seniority of male PIs is significantly higher than that of female PIs, with only 34% of the female PIs being professionally employed astronomers (compared to 53% for male PIs). A small, but statistically significant, gender-dependent behaviour is measured for the OPC referees: both genders show the same systematics, but they are larger for males than females. The PI female/male fraction is very close to 30/70; although far from parity, the fraction is higher than that observed, for instance, among IAU membership.