The main issue of this paper is to study the sign and direction of causality between two demographic variables --the fertility rate and the infant mortality rate - by using time series methodology. It is shown that a fall in fertility will decrease infant mortality below its normal level. It is also shown that fertility and infant mortality are not mutually independent but jointly determined. Therefore, when one constructs a model of the relationship between fertility and infant mortality,it is suggested that one should estimate a fertility equation in which infant mortality rate is an endogenous variable in a simultaneous equations system and vice versa.