The two-level superprocess is the diffusion limit of a two-level branching Brownian motion, where particles are grouped into superparticles which themselves duplicate or vanish according to a branching dynamic, in addition to the motion and branching of the individual particles themselves. We define three classes of initial states for two-level superprocesses and describe the corresponding patterns of longtime behavior, including two very different types of equilibria. Specifically, we show that two of these classes of initial states lead to longtime behavioral patterns in high dimensions that do not exist for ordinary, single-level branching systems or superprocesses. (Joint work with A.Greven.)