When protein synthesis is completely blocked from before fertilization, the sea urchin zygote arrests in first S phase and the paternal centrosome reduplicates multiple times. However, when protein synthesis is blocked starting in prophase of first mitosis, the zygote divides and the blastomeres arrest in a G1-like state. The centrosome inherited from this mitosis duplicates only once in each blastomere for reasons that are not understood. The late G1 rise in cyclin E/cdk2 kinase activity initiates centrosome duplication in mammalian cells and its activity is needed for centrosome duplication in Xenopus egg extracts. Since the half-time for cyclin E turnover is normally approximately 1 h in sea urchin zygotes, the different behaviors of centrosomes during G1 and S phase arrests could be due to differential losses of cyclin E and its associated kinase activities at these two arrest points. To better understand the mechanisms that limit centrosome duplication, we characterize the levels of cyclin E and its associated kinase activity at the S phase and G1 arrest points. We first demonstrate that cyclin E/cdk2 kinase activity is required for centrosome duplication and reduplication in sea urchin zygotes. Next we find that cyclin E levels and cyclin E/cdk2 kinase activities are both constitutively and equivalently elevated during both the S phase and G1 arrests. This indicates that centrosome duplication during the G1 arrest is limited by a block to reduplication under conditions permissive for duplication. The cytoplasmic conditions of S phase, however, abrogate this block to reduplication.