Haines, Munoz and van Gelderen have described the fitting of Gaussian ARIMA models to various discrete-valued time series related to births occurring during a 16-year period at Edendale Hospital in Natal, South Africa. This chapter describes the fitting of HM and Markov regression models to this series – Markov regression models, that is, in the sense in which that term is used by Zeger and Qaqish. These models are of course rather different from those fitted by Haines et al. in that theirs, being based on the normal distribution, are continuous-valued. The most important conclusion drawn from the discrete-valued models, and one which the Gaussian ARIMA models did not provide, is that there is a strong upward time trend in the proportion of the deliveries that are by Caesarean section. The models are nonseasonal; the Box-Jenkins methodology used found no seasonality in the Caesareans series.