In this two-part paper we examine some of the market characteristics of urban child-care services. Part 1 is concerned with theory. In it we review the contemporary child-care and preschool education service issue; consider questions of market efficiency and equity, and formulate these in a general equilibrium model which generates testable household labour-supply and service-supply functions. In part 2 we report on an empirical study in which aggregate versions of these functions are calibrated for the supply of labour from mothers with young children and for the supply of childminding services. We focus on the childminder sector, which is of interest as a personal social service that has traditionally been left to the private sector and as a private service with relatively easy entry and exit. These models yield interesting results which indicate on the one hand that access to child-care services is a binding constraint on female labour-market participation and on the other, that the supply of child-care services is quite unresponsive to demand.