The mechanics of DNA replication and cell cycling are well-characterized in model organisms, but less is known about these basic aspects of cell biology in early-diverging Apicomplexan parasites, which do not divide by canonical binary fission but undergo unconventional cycles. Schizogony in the malaria parasite, Plasmodium, generates ~16-24 new nuclei via independent, asynchronous rounds of genome replication prior to cytokinesis and little is known about the control of DNA replication that facilitates this. We have characterised replication dynamics in P. falciparum throughout schizogony, using DNA fibre labelling and combing to visualise replication forks at a single-molecule level. We show that origins are very closely spaced in Plasmodium compared to most model systems, and that replication dynamics vary across the course of schizogony, from faster synthesis rates and more widely-spaced origins through to slower synthesis rates and closer-spaced origins. This is the opposite of the pattern usually seen across S-phase in human cells, when a single genome is replicated. Replication forks also appear to stall at an unusually high rate throughout schizogony. Our work explores Plasmodium DNA replication in unprecedented detail and opens up tremendous scope for analysing cell cycle dynamics and developing interventions targetting this unique aspect of malaria biology.