"This paper considers the formulation, estimation and interpretation of microdynamic models of fertility. Our model explains parity choices, sterility, childlessness, interbirth intervals and initiation of pregnancy within a unified framework. We develop a general methodology for estimating the determinants of transition times to births of different orders. Our procedure incorporates time-varying explanatory variables and unobservables. We present conditions that justify conventional formulae relating hazards to survivor functions when time-varying variables enter hazards. We also consider the validity of widely-used piecemeal estimation strategies that focus on one birth at a time. We consider methods for selecting a best model among a class of non-nested models. Two criteria are set forth and used to evaluate the determinants of third births in Sweden."