We have reconstituted a eukaryotic leading/lagging strand replisome comprising 31 distinct polypeptides. This study identifies a process unprecedented in bacterial replisomes. While bacteria and phage simply recruit polymerases to the fork, we find that suppression mechanisms are used to position the distinct eukaryotic polymerases on their respective strands. Hence, Pol ε is active with CMG on the leading strand, but it is unable to function on the lagging strand, even when Pol δ is not present. Conversely, Pol δ-PCNA is the only enzyme capable of extending Okazaki fragments in the presence of Pols ε and α. We have shown earlier that Pol δ-PCNA is suppressed on the leading strand with CMG (<xref ref-type="bibr" rid="bib12">Georgescu et al., 2014</xref>). We propose that CMG, the 11-subunit helicase, is responsible for one or both of these suppression mechanisms that spatially control polymerase occupancy at the fork.