This paper examines the relationship between socioeconomic development and health and child mortality decline in developing countries which are in two different stages in the demographic transition. A measure of the transition "distance" travelled by a given country is developed and used to classify the countries into two groups: early and late transition countries. A path model linking socioeconomic and health variables and two measures of child mortality is developed and tested for the two groups of countries. The findings indicated that the network of linkages between independent and dependent variables are more significant in early transition than in late transition countries. The impact of health facilities on child mortality is large in early transition countries, but it declines as countries advance in their demographic transition. The reverse is true with respect to socioeconomic variables.