Phytoplankton are known to exhibit temporal variability in biomass and community composition. While physically driven sources of variability have been studied extensively, ecosystems often exhibit complicated intrinsic dynamics that are not as well understood. As a first step towards assessing the contribution of this intrinsic variability to the total variability in the ocean, we examine the temporal scales of intrinsic variability in a marine plankton model suitable for use in climate model projections. Our rationale is that a better understanding of the time scales over which intrinsic variability manifests could help in the attribution of observed variability. Our model includes multiple phytoplankton, dissolved inorganic nutrients, and zooplankton and supports two oscillatory mechanisms: "R-oscillations", corresponding to patterns of species succession and associated with changes in resources, and "Z-oscillations", corresponding to changes in total phytoplankton biomass due to predator-prey interactions. Over a wide range of model parameters, we found that while Z-oscillations typically occurred on time scales not exceeding 60 days, R-oscillations ranged from roughly 100 to 900 days under predation-free conditions, and R-oscillations occurred on longer time scales when interacting with Z-oscillations. Thus the two kinds of oscillations can be easily distinguished. At high grazing rates, we identified aperiodic cases where the dominant period never resolved, with distinct regimes emerging over decadal (or longer) time scales. These chaotic regime shifts are likely highly dependent on the model parameters and structure. More work must be done to understand how these oscillations interact with physical forcings.