The gonadotrophin-releasing hormone (GnRH) neurosecretory system involves both endocrine neurones and associated brain cells responsible for the control of GnRH release into the pituitary portal blood. Alternation between a pulsatile regime and the pre-ovulatory surge is the hallmark of GnRH secretion in ovarian cycles of female mammals. In previous studies, we have introduced a mathematical model of the pulse and surge GnRH generator and derived appropriate dynamics-based constraints on the model parameters, both to reproduce the right sequence of secretion events and to fulfil quantitative specifications on GnRH release. In the present study, we explain how these constraints amount to embedding time- and dose-dependent steroid control within the model. We further examine under which conditions the oestradiol-driven surge may be withdrawn by pre-surge progesterone administration and simulate both oestradiol and progesterone challenges in the pulsatile regime.