To describe changes in the maternal cerebral circulation and the external iliac arteries throughout pregnancy and the puerperium using the Laplace transform analysis of Doppler waveforms. A prospective longitudinal study. Department of Obstetrics and Gynaecology, Nottingham University Hospital. A cohort of 17 healthy women studied every four weeks from early pregnancy until term and up to three months postpartum. Pre-conception data were available for 10 subjects. Doppler signals were recorded from the internal carotid, middle cerebral and external iliac arteries. The waveforms were analysed using two different techniques: standard indices (systolic:diastolic ratio, pulsatility and resistance indices) and Laplace transform analysis, an alternative method of waveform shape analysis which may provide additional haemodynamic information. Vessel wall tone decreased at an early stage in pregnancy in the cerebral circulation and in the external iliac artery, but this rose again following delivery. The Laplace transform analysis techniques suggest dramatic eight-fold increases in downstream resistance within the external iliac artery in the second half of pregnancy. An increase in downstream resistance to flow also occurred in the internal carotid artery whereas more stable conditions were noted in the middle cerebral artery. Having a preliminary idea of the normal ranges for the Laplace transform analysis variables during pregnancy in a variety of maternal vessels, haemodynamic changes in pregnancies complicated by conditions, such as pre-eclampsia, can now be studied.