BACKGROUND: The low demand for maternal and child health services is a significant factor in Nigeria's high maternal death rate. This paper explores demand and supply-side determinants at the primary healthcare level, highlighting factors affecting provision and utilization. METHODS: This qualitative study was undertaken in Anambra state, southeast Nigeria. Anambra state was purposively chosen because a maternal and child health programme had just been implemented in the state. The three-delay model was used to analyze supply and demand factors that affect MCH services and improve access to care for pregnant women/mothers and newborns/infants. RESULT: The findings show that there were problems with both the demand and supply aspects of the programme and both were interlinked. For service users, their delays were connected to the constraints on the supply side. On the demand side, the delays include poor conditions of the facilities, the roads to the facilities are inaccessible, and equipment were lacking in the facilities. These delayed the utilisation of facilities. On the supply side, the delays include the absence of security (fence, security guard), poor citing of the facilities, inadequate accommodation, no emergency transport for referrals, and lack of trained staff to man equipment. These delayed the provision of services. CONCLUSION: Our findings show that there were problems with both the demand and supply aspects of the programme, and both were interlinked. For service users, their delays were connected to the constraints on the supply side.